Results of Asymptotic Approximations: Difference between revisions

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; Areas : [[2.1|2.1 Definitions and Elementary Properties]]<br>[[2.2|2.2 Transcendental Equations]]<br>[[2.3|2.3 Integrals of a Real Variable]]<br>[[2.4|2.4 Contour Integrals]]<br>[[2.5|2.5 Mellin Transform Methods]]<br>[[2.6|2.6 Distributional Methods]]<br>[[2.7|2.7 Differential Equations]]<br>[[2.8|2.8 Differential Equations with a Parameter]]<br>[[2.9|2.9 Difference Equations]]<br>[[2.10|2.10 Sums and Sequences]]<br>[[2.11|2.11 Remainder Terms; Stokes Phenomenon]]<br>
! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
</div>
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| [https://dlmf.nist.gov/2.1.E12 2.1.E12] || [[Item:Q697|<math>-1,\\ \ln@@{x},&\phantom{\realpart@@}\nu = -1,\\ x^{\nu+1}/(\nu+1),&\realpart@@{\nu}</math>]] || <code>- 1 , ln(x),</code> || <code>- 1 , Log[x],</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.2.E3 2.2.E3] || [[Item:Q710|<math>t^{2}-\ln@@{t} = y</math>]] || <code>(t)^(2)- ln(t) = y</code> || <code>(t)^(2)- Log[t] == y</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 36]<div class="mw-collapsible-content"><code>36/36]: [[3.344534892-3.141592654*I <- {t = -1.5, y = -1.5}</code><br><code>.344534892-3.141592654*I <- {t = -1.5, y = 1.5}</code><br><code>2.344534892-3.141592654*I <- {t = -1.5, y = -.5}</code><br><code>1.344534892-3.141592654*I <- {t = -1.5, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 36]<div class="mw-collapsible-content"><code>{Complex[3.3445348918918354, -3.141592653589793] <- {Rule[t, -1.5], Rule[y, -1.5]}</code><br><code>Complex[0.3445348918918356, -3.141592653589793] <- {Rule[t, -1.5], Rule[y, 1.5]}</code><br></div></div>
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| [https://dlmf.nist.gov/2.2.E5 2.2.E5] || [[Item:Q712|<math>t^{2} = y+\ln@@{t}</math>]] || <code>(t)^(2) = y + ln(t)</code> || <code>(t)^(2) == y + Log[t]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 36]<div class="mw-collapsible-content"><code>36/36]: [[3.344534892-3.141592654*I <- {t = -1.5, y = -1.5}</code><br><code>.344534892-3.141592654*I <- {t = -1.5, y = 1.5}</code><br><code>2.344534892-3.141592654*I <- {t = -1.5, y = -.5}</code><br><code>1.344534892-3.141592654*I <- {t = -1.5, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 36]<div class="mw-collapsible-content"><code>{Complex[3.3445348918918354, -3.141592653589793] <- {Rule[t, -1.5], Rule[y, -1.5]}</code><br><code>Complex[0.3445348918918356, -3.141592653589793] <- {Rule[t, -1.5], Rule[y, 1.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.3#Ex4 2.3#Ex4] || [[Item:Q734|<math>b_{0} = \frac{q_{0}}{\mu p_{0}^{\lambda/\mu}}</math>]] || <code>b[0] (q[0])/(mu*p(p[0])^(lambda/ mu))</code> || <code>Subscript[b, 0] Divide[Subscript[q, 0],\[Mu]*p(Subscript[p, 0])^(\[Lambda]/ \[Mu])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3#Ex5 2.3#Ex5] || [[Item:Q735|<math>b_{1} = \left(\frac{q_{1}}{\mu}-\frac{(\lambda+1)p_{1}q_{0}}{\mu^{2}p_{0}}\right)\frac{1}{p_{0}^{(\lambda+1)/\mu}}</math>]] || <code>b[1] = (1)/(p(p[0])^((lambda + 1)/ mu))</code> || <code>Subscript[b, 1] == Divide[1,p(Subscript[p, 0])^((\[Lambda]+ 1)/ \[Mu])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3#Ex6 2.3#Ex6] || [[Item:Q736|<math>b_{2} = \left(\frac{q_{2}}{\mu}-\frac{(\lambda+2)(p_{1}q_{1}+p_{2}q_{0})}{\mu^{2}p_{0}}+\frac{(\lambda+2)(\lambda+\mu+2)p_{1}^{2}q_{0}}{2\mu^{3}p_{0}^{2}}\right)\frac{1}{p_{0}^{(\lambda+2)/\mu}}</math>]] || <code>(1)/(p(p[0])^((lambda + 2)/ mu))</code> || <code>Divide[1,p(Subscript[p, 0])^((\[Lambda]+ 2)/ \[Mu])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3.E18 2.3.E18] || [[Item:Q737|<math>b_{s} = \frac{1}{\mu}\Residue_{t=a}\left[\frac{q(t)}{(p(t)-p(a))^{(\lambda+s)/\mu}}\right]</math>]] || <code>b[s] = (1)/(mu)*[t = a][(q*(t))/((p*(t)- p*(a))^((lambda + s)/ mu))]</code> || <code>Subscript[b, s] == Divide[1,\[Mu]]*Subscript[, t == a][Divide[q*(t),(p*(t)- p*(a))^((\[Lambda]+ s)/ \[Mu])]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3.E25 2.3.E25] || [[Item:Q744|<math>p(\alpha,t) = \tfrac{1}{2}w^{2}-aw+b</math>]] || <code>p*(alpha , t) = (1)/(2)*(w)^(2)- a*w + b</code> || <code>p*(\[Alpha], t) == Divide[1,2]*(w)^(2)- a*w + b</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3#Ex7 2.3#Ex7] || [[Item:Q745|<math>a = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}</math>]] || <code>a = (2*p*(alpha , 0)- 2*p*(alpha , alpha))^(1/ 2)</code> || <code>a == (2*p*(\[Alpha], 0)- 2*p*(\[Alpha], \[Alpha]))^(1/ 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3#Ex8 2.3#Ex8] || [[Item:Q746|<math>b = p(\alpha,0)</math>]] || <code>b = p*(alpha , 0)</code> || <code>b == p*(\[Alpha], 0)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/2.3.E27 2.3.E27] || [[Item:Q747|<math>w = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}+(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}</math>]] || <code>w = (2*p*(alpha , 0)- 2*p*(alpha , alpha))^(1/ 2)+(2*p*(alpha , t)- 2*p*(alpha , alpha))^(1/ 2)</code> || <code>w == (2*p*(\[Alpha], 0)- 2*p*(\[Alpha], \[Alpha]))^(1/ 2)+(2*p*(\[Alpha], t)- 2*p*(\[Alpha], \[Alpha]))^(1/ 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.3.E28 2.3.E28] || [[Item:Q748|<math>\deriv{w}{t} = +\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}</math>]] || <code>diff(w, t) = +(1)/((2*p*(alpha , t)- 2*p*(alpha , alpha))^(1/ 2))*diff(p*(alpha , t), t)</code> || <code>D[w, t] == +Divide[1,(2*p*(\[Alpha], t)- 2*p*(\[Alpha], \[Alpha]))^(1/ 2)]*D[p*(\[Alpha], t), t]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.3.E28 2.3.E28] || [[Item:Q748|<math>\deriv{w}{t} = -\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}</math>]] || <code>diff(w, t) = -(1)/((2*p*(alpha , t)- 2*p*(alpha , alpha))^(1/ 2))*diff(p*(alpha , t), t)</code> || <code>D[w, t] == -Divide[1,(2*p*(\[Alpha], t)- 2*p*(\[Alpha], \[Alpha]))^(1/ 2)]*D[p*(\[Alpha], t), t]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.4.E2 2.4.E2] || [[Item:Q755|<math>Q(z) = \int_{0}^{\infty}e^{-zt}q(t)\diff{t}</math>]] || <code>Q*(z) = int(exp(- z*t)*q*(t), t = 0..infinity)</code> || <code>Q*(z) == Integrate[Exp[- z*t]*q*(t), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [292 / 300]<div class="mw-collapsible-content"><code>292/300]: [[-.3660254032+1.366025404*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>Float(undefined)+.5000000004*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>1.732050808-1.000000001*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>Float(undefined)-.8660254040*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [284 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.3660254037844386, 1.3660254037844386] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.7320508075688774, -0.9999999999999999] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</code><br></div></div>
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| [https://dlmf.nist.gov/2.4.E5 2.4.E5] || [[Item:Q758|<math>q(t) = \frac{1}{2\pi i}\int_{\sigma-i\infty}^{\sigma+i\infty}e^{tz}Q(z)\diff{z}</math>]] || <code>q*(t) = (1)/(2*Pi*I)*int(exp(t*z)*Q*(z), z = sigma - I*infinity..sigma + I*infinity)</code> || <code>q*(t) == Divide[1,2*Pi*I]*Integrate[Exp[t*z]*Q*(z), {z, \[Sigma]- I*Infinity, \[Sigma]+ I*Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.299038106+.7500000000*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, t = 1.5}</code><br><code>.4330127020+.2500000000*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, t = .5}</code><br><code>1.732050808+1.*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, t = 2}</code><br><code>1.299038106+.7500000000*I <- {Q = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, sigma = -1/2+1/2*I*3^(1/2), t = 1.5}</code><br>... skip entries to safe data<br></div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.4#Ex1 2.4#Ex1] || [[Item:Q764|<math>p(t) = p(a)+\sum_{s=0}^{\infty}p_{s}(t-a)^{s+\mu}</math>]] || <code>p*(t) = p*(a)+ sum(p[s]*(t - a)^(s + mu), s = 0..infinity)</code> || <code>p*(t) == p*(a)+ Sum[Subscript[p, s]*(t - a)^(s + \[Mu]), {s, 0, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/2.4#Ex2 2.4#Ex2] || [[Item:Q765|<math>q(t) = \sum_{s=0}^{\infty}q_{s}(t-a)^{s+\lambda-1}</math>]] || <code>q*(t) = sum(q[s]*(t - a)^(s + lambda - 1), s = 0..infinity)</code> || <code>q*(t) == Sum[Subscript[q, s]*(t - a)^(s + \[Lambda]- 1), {s, 0, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/2.4.E13 2.4.E13] || [[Item:Q767|<math>|\theta+\mu\omega+\phase@@{p_{0}}| \leq \tfrac{1}{2}\pi</math>]] || <code>abs(theta + mu*omega + argument(p[0])) <= (1)/(2)*Pi</code> || <code>Abs[\[Theta]+ \[Mu]*\[Omega]+ Arg[Subscript[p, 0]]] <= Divide[1,2]*Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [174 / 300]<div class="mw-collapsible-content"><code>174/300]: [[2.331674280 <= 1.570796327 <- {mu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, p[0] = 1/2*3^(1/2)+1/2*I}</code><br><code>3.720287017 <= 1.570796327 <- {mu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, p[0] = -1/2+1/2*I*3^(1/2)}</code><br><code>1.852957222 <= 1.570796327 <- {mu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, p[0] = -1/2*3^(1/2)-1/2*I}</code><br><code>4.710057957 <= 1.570796327 <- {mu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, p[0] = -1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [211 / 300]<div class="mw-collapsible-content"><code>{False <- {Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>False <- {Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.4.E14 2.4.E14] || [[Item:Q768|<math>I(z) = \int_{t_{0}}^{b}e^{-zp(t)}q(t)\diff{t}-\int_{t_{0}}^{a}e^{-zp(t)}q(t)\diff{t}</math>]] || <code>I*(z) = int(exp(- z*p*(t))*q*(t), t = t[0]..b)- int(exp(- z*p*(t))*q*(t), t = t[0]..a)</code> || <code>I*(z) == Integrate[Exp[- z*p*(t)]*q*(t), {t, Subscript[t, 0], b}, GenerateConditions->None]- Integrate[Exp[- z*p*(t)]*q*(t), {t, Subscript[t, 0], a}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/2.4.E18 2.4.E18] || [[Item:Q773|<math>p(\alpha,t) = \tfrac{1}{3}w^{3}+aw^{2}+bw+c</math>]] || <code>p*(alpha , t) = (1)/(3)*(w)^(3)+ a*(w)^(2)+ b*w + c</code> || <code>p*(\[Alpha], t) == Divide[1,3]*(w)^(3)+ a*(w)^(2)+ b*w + c</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/2.4.E20 2.4.E20] || [[Item:Q775|<math>q(\alpha,t)\deriv{t}{w} = q(\alpha,t)\frac{w^{2}+2aw+b}{\ipderiv{p(\alpha,t)}{t}}</math>]] || <code>q*(alpha , t)* diff(t, w) = q*(alpha , t)*((w)^(2)+ 2*a*w + b)/(diff(p*(alpha , t), t))</code> || <code>q*(\[Alpha], t)* D[t, w] == q*(\[Alpha], t)*Divide[(w)^(2)+ 2*a*w + b,D[p*(\[Alpha], t), t]]</code> || Error || Failure || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.4.E21 2.4.E21] || [[Item:Q776|<math>w = z^{-1/3}v-a</math>]] || <code>w = (z)^(- 1/ 3)* v - a</code> || <code>w == (z)^(- 1/ 3)* v - a</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.5.E8 2.5.E8] || [[Item:Q784|<math>I(x) = \int_{0}^{\infty}\frac{\BesselJ{\nu}^{2}@{xt}}{1+t}\diff{t}</math>]] || <code>I*(x) = int(((BesselJ(nu, x*t))^(2))/(1 + t), t = 0..infinity)</code> || <code>I*(x) == Integrate[Divide[(BesselJ[\[Nu], x*t])^(2),1 + t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><code>90/90]: [[Float(infinity)+Float(infinity)*I <- {I = 1/2*3^(1/2)+1/2*I, nu = 1.5, x = 1.5}</code><br><code>Float(infinity)+Float(infinity)*I <- {I = 1/2*3^(1/2)+1/2*I, nu = 1.5, x = .5}</code><br><code>Float(infinity)+Float(infinity)*I <- {I = 1/2*3^(1/2)+1/2*I, nu = 1.5, x = 2}</code><br><code>Float(infinity)+.7500000000*I <- {I = 1/2*3^(1/2)+1/2*I, nu = .5, x = 1.5}</code><br>... skip entries to safe data<br></div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.5.E12 2.5.E12] || [[Item:Q788|<math>a_{n} = \frac{2^{n-1}\EulerGamma@{\nu+\tfrac{1}{2}n}}{\EulerGamma^{2}@{1-\tfrac{1}{2}n}\EulerGamma@{1+\nu-\tfrac{1}{2}n}\EulerGamma@{n}}</math>]] || <code>a[n] = ((2)^(n - 1)* GAMMA(nu +(1)/(2)*n))/((GAMMA(1 -(1)/(2)*n))^(2)* GAMMA(1 + nu -(1)/(2)*n)*GAMMA(n))</code> || <code>Subscript[a, n] == Divide[(2)^(n - 1)* Gamma[\[Nu]+Divide[1,2]*n],(Gamma[1 -Divide[1,2]*n])^(2)* Gamma[1 + \[Nu]-Divide[1,2]*n]*Gamma[n]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5477155179+.5000000000*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.8660254040+.5000000000*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.8262366682+.3621677762*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>-.8183098861+.8660254040*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.5477155176006481, 0.49999999999999994] <- {Rule[n, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[n, 2], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.5.E13 2.5.E13] || [[Item:Q789|<math>b_{n} = -a_{n}\left(\ln@@{2}+\tfrac{1}{2}\digamma@{\nu+\tfrac{1}{2}n}+\digamma@{1-\tfrac{1}{2}n}+\tfrac{1}{2}\digamma@{1+\nu-\tfrac{1}{2}n}-\digamma@{n}\right)</math>]] || <code>b[n] = - a[n]*(ln(2)+(1)/(2)*Psi(nu +(1)/(2)*n)+ Psi(1 -(1)/(2)*n)+(1)/(2)*Psi(1 + nu -(1)/(2)*n)- Psi(n))</code> || <code>Subscript[b, n] == - Subscript[a, n]*(Log[2]+Divide[1,2]*PolyGamma[\[Nu]+Divide[1,2]*n]+ PolyGamma[1 -Divide[1,2]*n]+Divide[1,2]*PolyGamma[1 + \[Nu]-Divide[1,2]*n]- PolyGamma[n])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.386290893e-1+.5914576348*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, b[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, b[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.719377583e-1+1.226073019*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, b[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>-1.327396315+.9574830388*I <- {nu = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, b[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.0386290885385151, 0.59145763437721] <- {Rule[n, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.3273963152459234, 0.9574830381616488] <- {Rule[n, 1], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.5.E24 2.5.E24] || [[Item:Q800|<math>h_{2}(t) = h(t)-h_{1}(t)</math>]] || <code>h[2]*(t) = h*(t)- h[1]*(t)</code> || <code>Subscript[h, 2]*(t) == h*(t)- Subscript[h, 1]*(t)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.5.E30 2.5.E30] || [[Item:Q806|<math>I_{jk}(x) = \int_{0}^{\infty}f_{j}(t)h_{k}(xt)\diff{t}</math>]] || <code>I[j*k]*(x) = int(f[j]*(t)* h[k]*(x*t), t = 0..infinity)</code> || <code>Subscript[I, j*k]*(x) == Integrate[Subscript[f, j]*(t)* Subscript[h, k]*(x*t), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[Float(infinity)+Float(infinity)*I <- {x = 1.5, I[j*k] = 1/2*3^(1/2)+1/2*I, f[j] = 1/2*3^(1/2)+1/2*I, h[k] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {x = 1.5, I[j*k] = 1/2*3^(1/2)+1/2*I, f[j] = 1/2*3^(1/2)+1/2*I, h[k] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {x = 1.5, I[j*k] = 1/2*3^(1/2)+1/2*I, f[j] = 1/2*3^(1/2)+1/2*I, h[k] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {x = 1.5, I[j*k] = 1/2*3^(1/2)+1/2*I, f[j] = 1/2*3^(1/2)+1/2*I, h[k] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.59977280929447116972275470162594*^+83839, -2.77088778626521950864048398971341*^+83839] <- {Rule[j, 1], Rule[k, 1], Rule[x, 1.5], Rule[Subscript[Complex[0, 1], Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.59977280929447116972275470162594*^+83839, -2.77088778626521950864048398971341*^+83839] <- {Rule[j, 1], Rule[k, 2], Rule[x, 1.5], Rule[Subscript[Complex[0, 1], Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.5.E31 2.5.E31] || [[Item:Q807|<math>I_{21}(x) = 0</math>]] || <code>I[21]*(x) = 0</code> || <code>Subscript[I, 21]*(x) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.5.E33 2.5.E33] || [[Item:Q809|<math>I_{jk}(x) = \frac{1}{2\pi i}\int_{p_{jk}-i\infty}^{p_{jk}+i\infty}x^{-z}G_{jk}(z)\diff{z}</math>]] || <code>I[j*k]*(x) = (1)/(2*Pi*I)*int((x)^(-(x + y*I))* G[j*k]*((x + y*I)), (x + y*I) = p[j*k]- I*infinity..p[j*k]+ I*infinity)</code> || <code>Subscript[I, j*k]*(x) == Divide[1,2*Pi*I]*Integrate[(x)^(-(x + y*I))* Subscript[G, j*k]*((x + y*I)), {(x + y*I), Subscript[p, j*k]- I*Infinity, Subscript[p, j*k]+ I*Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[1.299038105676658, 0.7499999999999999], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Complex[1.0861132213040667, 0.3920349523216481] <- {Complex[1.5, -1.5], DirectedInfinity[Complex[0, -1]], DirectedInfinity[Complex[0, 1]]}]]], {Rule[j, 1], Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[Complex[0, 1], Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[G, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[1.299038105676658, 0.7499999999999999], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Complex[1.0861132213040667, 0.3920349523216481] <- {Complex[1.5, -1.5], DirectedInfinity[Complex[0, -1]], DirectedInfinity[Complex[0, 1]]}]]], {Rule[j, 1], Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[Complex[0, 1], Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[G, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.5.E35 2.5.E35] || [[Item:Q811|<math>I_{jk}(x) = \sum_{p_{jk}<\realpart@@{z}<q_{jk}}\Residue\left[-x^{-z}G_{jk}(z)\right]+E_{jk}(x)</math>]] || <code>I[j*k]*(x) = sum(*[- (x)^(-(x + y*I))* G[j*k]*((x + y*I))], Re(x + y*I) = p[j*k] + 1..q[j*k] - 1)+ E[j*k]*(x)</code> || <code>Subscript[I, j*k]*(x) == Sum[*[- (x)^(-(x + y*I))* Subscript[G, j*k]*((x + y*I))], {Re[x + y*I], Subscript[p, j*k] + 1, Subscript[q, j*k] - 1}, GenerateConditions->None]+ Subscript[E, j*k]*(x)</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.5.E36 2.5.E36] || [[Item:Q812|<math>E_{jk}(x) = \frac{1}{2\pi i}\int_{q_{jk}-i\infty}^{q_{jk}+i\infty}x^{-z}G_{jk}(z)\diff{z}</math>]] || <code>E[j*k]*(x) = (1)/(2*Pi*I)*int((x)^(-(x + y*I))* G[j*k]*((x + y*I)), (x + y*I) = q[j*k]- I*infinity..q[j*k]+ I*infinity)</code> || <code>Subscript[E, j*k]*(x) == Divide[1,2*Pi*I]*Integrate[(x)^(-(x + y*I))* Subscript[G, j*k]*((x + y*I)), {(x + y*I), Subscript[q, j*k]- I*Infinity, Subscript[q, j*k]+ I*Infinity}, GenerateConditions->None]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[1.299038105676658, 0.7499999999999999], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Complex[1.0861132213040667, 0.3920349523216481] <- {Complex[1.5, -1.5], DirectedInfinity[Complex[0, -1]], DirectedInfinity[Complex[0, 1]]}]]], {Rule[j, 1], Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[E, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[G, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[q, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[1.299038105676658, 0.7499999999999999], Times[Complex[0.0, 0.15915494309189535], NIntegrate[Complex[1.0861132213040667, 0.3920349523216481] <- {Complex[1.5, -1.5], DirectedInfinity[Complex[0, -1]], DirectedInfinity[Complex[0, 1]]}]]], {Rule[j, 1], Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[E, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[G, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[q, Times[j, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.5.E39 2.5.E39] || [[Item:Q815|<math>I_{j}(x) = \int_{0}^{\infty}e^{-t}h_{j}(xt)\diff{t}</math>]] || <code>I[j]*(x) = int(exp(- t)*h[j]*(x*t), t = 0..infinity)</code> || <code>Subscript[I, j]*(x) == Integrate[Exp[- t]*Subscript[h, j]*(x*t), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 300]<div class="mw-collapsible-content"><code>270/300]: [[2.049038106-.5490381060*I <- {x = 1.5, I[j] = 1/2*3^(1/2)+1/2*I, h[j] = -1/2+1/2*I*3^(1/2), j = 1, j = 1}</code><br><code>2.049038106-.5490381060*I <- {x = 1.5, I[j] = 1/2*3^(1/2)+1/2*I, h[j] = -1/2+1/2*I*3^(1/2), j = 2, j = 1}</code><br><code>2.049038106-.5490381060*I <- {x = 1.5, I[j] = 1/2*3^(1/2)+1/2*I, h[j] = -1/2+1/2*I*3^(1/2), j = 3, j = 1}</code><br><code>.5490381060+2.049038106*I <- {x = 1.5, I[j] = 1/2*3^(1/2)+1/2*I, h[j] = 1/2-1/2*I*3^(1/2), j = 1, j = 1}</code><br>... skip entries to safe data<br></div></div> || Skip - No test values generated
|-
| [https://dlmf.nist.gov/2.5.E46 2.5.E46] || [[Item:Q822|<math>\Residue_{z=k}\left[-\zeta^{z-1}\EulerGamma@{1-z}\pi\csc@{\pi z}\right] = \left(-\ln@@{\zeta}+\digamma@{k}\right)\dfrac{\zeta^{k-1}}{(k-1)!}</math>]] || <code>[z = k][- (zeta)^(z - 1)* GAMMA(1 - z)*Pi*csc(Pi*z)] = (- ln(zeta)+ Psi(k))*((zeta)^(k - 1))/(factorial(k - 1))</code> || <code>Subscript[, z == k][- \[Zeta]^(z - 1)* Gamma[1 - z]*Pi*Csc[Pi*z]] == (- Log[\[Zeta]]+ PolyGamma[k])*Divide[\[Zeta]^(k - 1),(k - 1)!]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [50 / 50]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5772156649015329, 0.5235987755982988], Subscript[Null, False][Complex[1.288067451091007, -0.9403972809133088]]] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.5772156649015329, 2.0943951023931953], Subscript[Null, False][Complex[0.48475507921827343, -0.541984224121457]]] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.6.E1 2.6.E1] || [[Item:Q826|<math>S(x) = \int_{0}^{\infty}\frac{1}{(1+t)^{1/3}(x+t)}\diff{t}</math>]] || <code>S*(x) = int((1)/((1 + t)^(1/ 3)*(x + t)), t = 0..infinity)</code> || <code>S*(x) == Integrate[Divide[1,(1 + t)^(1/ 3)*(x + t)], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[-1.405894671+.7500000000*I <- {S = 1/2*3^(1/2)+1/2*I, x = 1.5}</code><br><code>-3.111297626+.2500000000*I <- {S = 1/2*3^(1/2)+1/2*I, x = .5}</code><br><code>-.774895738+1.*I <- {S = 1/2*3^(1/2)+1/2*I, x = 2}</code><br><code>-3.454932777+1.299038106*I <- {S = -1/2+1/2*I*3^(1/2), x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[-1.4058946699058708, 0.7499999999999999] <- {Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</code><br><code>Complex[-3.1112976262861083, 0.24999999999999997] <- {Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.6.E2 2.6.E2] || [[Item:Q827|<math>(1+t)^{-1/3} = \sum_{s=0}^{\infty}\binom{-\frac{1}{3}}{s}t^{-s-(1/3)}</math>]] || <code>(1 + t)^(- 1/ 3) = sum(binomial(-(1)/(3),s)*(t)^(- s -(1/ 3)), s = 0..infinity)</code> || <code>(1 + t)^(- 1/ 3) == Sum[Binomial[-Divide[1,3],s]*(t)^(- s -(1/ 3)), {s, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 6]<div class="mw-collapsible-content"><code>1/6]: [[Float(infinity)+Float(infinity)*I <- {t = -.5}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 6]<div class="mw-collapsible-content"><code>{Complex[1.8898815748423095, 1.0911236359717216] <- {Rule[t, -0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.6.E4 2.6.E4] || [[Item:Q829|<math>\int_{0}^{\infty}\frac{t^{\alpha-1}}{(x+t)^{\alpha+\beta}}\diff{t} = \frac{\EulerGamma@{\alpha}\EulerGamma@{\beta}}{\EulerGamma@{\alpha+\beta}}\frac{1}{x^{\beta}}</math>]] || <code>int(((t)^(alpha - 1))/((x + t)^(alpha + beta)), t = 0..infinity) = (GAMMA(alpha)*GAMMA(beta))/(GAMMA(alpha + beta))*(1)/((x)^(beta))</code> || <code>Integrate[Divide[(t)^(\[Alpha]- 1),(x + t)^(\[Alpha]+ \[Beta])], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Alpha]]*Gamma[\[Beta]],Gamma[\[Alpha]+ \[Beta]]]*Divide[1,(x)^\[Beta]]</code> || Failure || Successful || Successful [Tested: 27] || Successful [Tested: 27]
|-
| [https://dlmf.nist.gov/2.6.E5 2.6.E5] || [[Item:Q830|<math>\int_{0}^{\infty}\frac{t^{-s-(1/3)}}{x+t}\diff{t} = \frac{2\pi}{\sqrt{3}}\frac{(-1)^{s}}{x^{s+(1/3)}}</math>]] || <code>int(((t)^(- s -(1/ 3)))/(x + t), t = 0..infinity) = (2*Pi)/(sqrt(3))*((- 1)^(s))/((x)^(s +(1/ 3)))</code> || <code>Integrate[Divide[(t)^(- s -(1/ 3)),x + t], {t, 0, Infinity}, GenerateConditions->None] == Divide[2*Pi,Sqrt[3]]*Divide[(- 1)^(s),(x)^(s +(1/ 3))]</code> || Failure || Failure || Skipped - Because timed out || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/2.6.E22 2.6.E22] || [[Item:Q847|<math>\phi_{\varepsilon}(t) = \frac{e^{-\varepsilon t}}{t+z}</math>]] || <code>phi[varepsilon]*(t) = (exp(- varepsilon*t))/(t + z)</code> || <code>Subscript[\[Phi], \[CurlyEpsilon]]*(t) == Divide[Exp[- \[CurlyEpsilon]*t],t + z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.6.E30 2.6.E30] || [[Item:Q856|<math>R_{n}(z) = \frac{(-1)^{n}}{z^{n}}\int_{0}^{\infty}\frac{\tau^{n}f_{n}(\tau)}{\tau+z}\diff{\tau}</math>]] || <code>R[n]*(z) = ((- 1)^(n))/((z)^(n))*int(((tau)^(n)* f[n]*(tau))/(tau + z), tau = 0..infinity)</code> || <code>Subscript[R, n]*(z) == Divide[(- 1)^(n),(z)^(n)]*Integrate[Divide[\[Tau]^(n)* Subscript[f, n]*(\[Tau]),\[Tau]+ z], {\[Tau], 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, f[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>DirectedInfinity[] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.6.E41 2.6.E41] || [[Item:Q867|<math>f = \sum_{s=0}^{n-1}a_{s}t^{-s-\alpha}-\sum_{s=1}^{n}c_{s}\Diracdelta^{(s-1)}+f_{n}</math>]] || <code>f = sum(a[s]*(t)^(- s - alpha), s = 0..n - 1)- sum(c[s]*subs( temp=+, diff( Dirac(temp), temp$(s - 1) ) )*f[n], s = 1..n)</code> || <code>f == Sum[Subscript[a, s]*(t)^(- s - \[Alpha]), {s, 0, n - 1}, GenerateConditions->None]- Sum[Subscript[c, s]*(D[DiracDelta[temp], {temp, s - 1}]/.temp-> +)*Subscript[f, n], {s, 1, n}, GenerateConditions->None]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.6.E42 2.6.E42] || [[Item:Q868|<math>f = \sum_{s=0}^{n-1}a_{s}t^{-s-1}-\sum_{s=1}^{n}d_{s}\Diracdelta^{(s-1)}+f_{n}</math>]] || <code>f = sum(a[s]*(t)^(- s - 1), s = 0..n - 1)- sum(d[s]*subs( temp=+, diff( Dirac(temp), temp$(s - 1) ) )*f[n], s = 1..n)</code> || <code>f == Sum[Subscript[a, s]*(t)^(- s - 1), {s, 0, n - 1}, GenerateConditions->None]- Sum[Subscript[d, s]*(D[DiracDelta[temp], {temp, s - 1}]/.temp-> +)*Subscript[f, n], {s, 1, n}, GenerateConditions->None]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.6.E47 2.6.E47] || [[Item:Q873|<math>\delta_{n}(x) = \sum_{j=0}^{n}\binom{n}{j}\frac{\EulerGamma@{\mu+1}}{\EulerGamma@{\mu+1-j}}I^{\mu}\left(t^{n-j}f_{n,j}\right)(x)</math>]] || <code>delta[n]*(x) = sum(binomial(n,j)*(GAMMA(mu + 1))/(GAMMA(mu + 1 - j))*(I)^(mu)*((t)^(n - j)* f[n , j])*(x), j = 0..n)</code> || <code>Subscript[\[Delta], n]*(x) == Sum[Binomial[n,j]*Divide[Gamma[\[Mu]+ 1],Gamma[\[Mu]+ 1 - j]]*(I)^\[Mu]*((t)^(n - j)* Subscript[f, n , j])*(x), {j, 0, n}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[2.186980427+1.033699533*I <- {I = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -1.5, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n,j] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.6751758732+2.165771578*I <- {I = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -1.5, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n,j] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>-.429437374-4.142136088*I <- {I = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -1.5, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n,j] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>1.015338573+1.637942321*I <- {I = 1/2*3^(1/2)+1/2*I, delta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -1.5, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n,j] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.6.E50 2.6.E50] || [[Item:Q876|<math>f_{n}(t) = (-1)^{n}\frac{t^{1-n-\alpha}}{1+t}</math>]] || <code>f[n]*(t) = (- 1)^(n)*((t)^(1 - n - alpha))/(1 + t)</code> || <code>Subscript[f, n]*(t) == (- 1)^(n)*Divide[(t)^(1 - n - \[Alpha]),1 + t]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.6.E53 2.6.E53] || [[Item:Q879|<math>{\left|\delta_{n}(x)\right|} \leq \frac{\EulerGamma@{\mu+1}\EulerGamma@{1-\alpha}}{\EulerGamma@{\mu+1-\alpha}\EulerGamma@{n+\alpha}}\*\sum_{j=0}^{n}\dbinom{n}{j}\frac{\EulerGamma@{n+\alpha-j}}{\left|\EulerGamma@{\mu+1-j}\right|}x^{\mu-\alpha}</math>]] || <code>abs(delta[n]*(x)) <= (GAMMA(mu + 1)*GAMMA(1 - alpha))/(GAMMA(mu + 1 - alpha)*GAMMA(n + alpha))* sum(binomial(n,j)*(GAMMA(n + alpha - j))/(abs(GAMMA(mu + 1 - j)))*(x)^(mu - alpha), j = 0..n)</code> || <code>Abs[Subscript[\[Delta], n]*(x)] <= Divide[Gamma[\[Mu]+ 1]*Gamma[1 - \[Alpha]],Gamma[\[Mu]+ 1 - \[Alpha]]*Gamma[n + \[Alpha]]]* Sum[Binomial[n,j]*Divide[Gamma[n + \[Alpha]- j],Abs[Gamma[\[Mu]+ 1 - j]]]*(x)^(\[Mu]- \[Alpha]), {j, 0, n}, GenerateConditions->None]</code> || Failure || Failure || Successful [Tested: 300] || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.6.E56 2.6.E56] || [[Item:Q882|<math>h(t) = \sum_{s=0}^{n-1}b_{s}t^{-s-\beta}+h_{n}(t)</math>]] || <code>h*(t) = sum(b[s]*(t)^(- s - beta), s = 0..n - 1)+ h[n]*(t)</code> || <code>h*(t) == Sum[Subscript[b, s]*(t)^(- s - \[Beta]), {s, 0, n - 1}, GenerateConditions->None]+ Subscript[h, n]*(t)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.6.E59 2.6.E59] || [[Item:Q885|<math>\int_{0}^{\infty}t^{\lambda}\diff{t} = 0</math>]] || <code>int((t)^(lambda), t = 0..infinity) = 0</code> || <code>Integrate[(t)^\[Lambda], {t, 0, Infinity}, GenerateConditions->None] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>10/10]: [[Float(undefined) <- {lambda = 1/2*3^(1/2)+1/2*I, lambda = 1+I}</code><br><code>Float(undefined) <- {lambda = -1/2+1/2*I*3^(1/2), lambda = 1+I}</code><br><code>Float(undefined) <- {lambda = 1/2-1/2*I*3^(1/2), lambda = 1+I}</code><br><code>Float(undefined) <- {lambda = -1/2*3^(1/2)-1/2*I, lambda = 1+I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><code>{Complex[2.105124266860741235376093541450691432144791*^+55894, -3.724980817286574983657738842232337454559011*^+55894] <- {Rule[λ, Complex[1, 1]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.6#Ex2 2.6#Ex2] || [[Item:Q889|<math>\delta_{n}(x) = \int_{0}^{\infty}f_{n}(t)h_{n}(xt)\diff{t}</math>]] || <code>delta[n]*(x) = int(f[n]*(t)* h[n]*(x*t), t = 0..infinity)</code> || <code>Subscript[\[Delta], n]*(x) == Integrate[Subscript[f, n]*(t)* Subscript[h, n]*(x*t), {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[Float(infinity)+Float(infinity)*I <- {delta = 1/2*3^(1/2)+1/2*I, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, h[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {delta = 1/2*3^(1/2)+1/2*I, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, h[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {delta = 1/2*3^(1/2)+1/2*I, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, h[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {delta = 1/2*3^(1/2)+1/2*I, x = 1.5, delta[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, h[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.59977280929447116972275470162594*^+83839, -2.77088778626521950864048398971341*^+83839] <- {Rule[n, 1], Rule[x, 1.5], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[δ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.59977280929447116972275470162594*^+83839, -2.77088778626521950864048398971341*^+83839] <- {Rule[n, 2], Rule[x, 1.5], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[δ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E3 2.7.E3] || [[Item:Q893|<math>Q(\alpha)\defeq\alpha(\alpha-1)+f_{0}\alpha+g_{0} = 0</math>]] || <code>Q*(alpha) = alpha*(alpha - 1)+ f[0]*alpha + g[0] = 0</code> || <code>Q*(\[Alpha]) == \[Alpha]*(\[Alpha]- 1)+ Subscript[f, 0]*\[Alpha]+ Subscript[g, 0] == 0</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><code>{False <- {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[f, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>False <- {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[f, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E4 2.7.E4] || [[Item:Q894|<math>w_{j}(z) = (z-z_{0})^{\alpha_{j}}\sum_{s=0}^{\infty}a_{s,j}(z-z_{0})^{s}</math>]] || <code>w[j]*(z) = (z - z[0])^(alpha[j])* sum(a[s , j]*(z - z[0])^(s), s = 0..infinity)</code> || <code>Subscript[w, j]*(z) == (z - Subscript[z, 0])^(Subscript[\[Alpha], j])* Sum[Subscript[a, s , j]*(z - Subscript[z, 0])^(s), {s, 0, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E5 2.7.E5] || [[Item:Q895|<math>Q(\alpha_{j}+s)a_{s,j} = -\sum_{r=0}^{s-1}\left((\alpha_{j}+r)f_{s-r}+g_{s-r}\right)a_{r,j}</math>]] || <code>Q*(alpha[j]+ s)* a[s , j] = - sum(((alpha[j]+ r)*f[s - r]+ g[s - r])* a[r , j], r = 0..s - 1)</code> || <code>Q*(Subscript[\[Alpha], j]+ s)* Subscript[a, s , j] == - Sum[((Subscript[\[Alpha], j]+ r)*Subscript[f, s - r]+ Subscript[g, s - r])* Subscript[a, r , j], {r, 0, s - 1}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E9 2.7.E9] || [[Item:Q900|<math>\lambda^{2}+f_{0}\lambda+g_{0} = 0</math>]] || <code>(lambda)^(2)+ f[0]*lambda + g[0] = 0</code> || <code>\[Lambda]^(2)+ Subscript[f, 0]*\[Lambda]+ Subscript[g, 0] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E10 2.7.E10] || [[Item:Q901|<math>\mu_{j} = -(f_{1}\lambda_{j}+g_{1})/(f_{0}+2\lambda_{j})</math>]] || <code>mu[j] = -(f[1]*lambda[j]+ g[1])/(f[0]+ 2*lambda[j])</code> || <code>Subscript[\[Mu], j] == -(Subscript[f, 1]*Subscript[\[Lambda], j]+ Subscript[g, 1])/(Subscript[f, 0]+ 2*Subscript[\[Lambda], j])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E11 2.7.E11] || [[Item:Q902|<math>(f_{0}+2\lambda_{j})sa_{s,j} = (s-\mu_{j})(s-1-\mu_{j})a_{s-1,j}+\sum_{r=1}^{s}\left(\lambda_{j}f_{r+1}+g_{r+1}-(s-r-\mu_{j})f_{r}\right)a_{s-r,j}</math>]] || <code>(f[0]+ 2*lambda[j])* s*a[s , j] = (s - mu[j])*(s - 1 - mu[j])* a[s - 1 , j]+ sum((lambda[j]*f[r + 1]+ g[r + 1]-(s - r - mu[j])*f[r])* a[s - r , j], r = 1..s)</code> || <code>(Subscript[f, 0]+ 2*Subscript[\[Lambda], j])* s*Subscript[a, s , j] == (s - Subscript[\[Mu], j])*(s - 1 - Subscript[\[Mu], j])* Subscript[a, s - 1 , j]+ Sum[(Subscript[\[Lambda], j]*Subscript[f, r + 1]+ Subscript[g, r + 1]-(s - r - Subscript[\[Mu], j])*Subscript[f, r])* Subscript[a, s - r , j], {r, 1, s}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E15 2.7.E15] || [[Item:Q906|<math>-\tfrac{3}{2}\pi+\delta \leq \phase@{(\lambda_{2}-\lambda_{1})z}</math>]] || <code>-(3)/(2)*Pi + delta <= argument((lambda[2]- lambda[1])* z)</code> || <code>-Divide[3,2]*Pi + \[Delta] <= Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])* z]</code> || Failure || Failure || Successful [Tested: 300] || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{LessEqual[Complex[-3.846363576600251, 0.49999999999999994], 0.0] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[Complex[-3.846363576600251, 0.49999999999999994], -2.8797932657906435] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E15 2.7.E15] || [[Item:Q906|<math>\phase@{(\lambda_{2}-\lambda_{1})z} \leq \tfrac{3}{2}\pi-\delta</math>]] || <code>argument((lambda[2]- lambda[1])* z) <= (3)/(2)*Pi - delta</code> || <code>Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])* z] <= Divide[3,2]*Pi - \[Delta]</code> || Failure || Failure || Successful [Tested: 300] || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{LessEqual[0.0, Complex[3.846363576600251, -0.49999999999999994]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[-2.8797932657906435, Complex[3.846363576600251, -0.49999999999999994]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E16 2.7.E16] || [[Item:Q907|<math>-\tfrac{1}{2}\pi+\delta \leq \phase@{(\lambda_{2}-\lambda_{1})z}</math>]] || <code>-(1)/(2)*Pi + delta <= argument((lambda[2]- lambda[1])* z)</code> || <code>-Divide[1,2]*Pi + \[Delta] <= Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])* z]</code> || Failure || Failure || Successful [Tested: 300] || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{LessEqual[Complex[-0.7047709230104579, 0.49999999999999994], 0.0] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[Complex[-0.7047709230104579, 0.49999999999999994], -2.8797932657906435] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E16 2.7.E16] || [[Item:Q907|<math>\phase@{(\lambda_{2}-\lambda_{1})z} \leq \tfrac{5}{2}\pi-\delta</math>]] || <code>argument((lambda[2]- lambda[1])* z) <= (5)/(2)*Pi - delta</code> || <code>Arg[(Subscript[\[Lambda], 2]- Subscript[\[Lambda], 1])* z] <= Divide[5,2]*Pi - \[Delta]</code> || Failure || Failure || Successful [Tested: 300] || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{LessEqual[0.0, Complex[6.987956230190044, -0.49999999999999994]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[-2.8797932657906435, Complex[6.987956230190044, -0.49999999999999994]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[λ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7#Ex5 2.7#Ex5] || [[Item:Q908|<math>w_{1}(z) = e^{2\pi i\mu_{1}}w_{1}(ze^{-2\pi i})+C_{1}w_{2}(z)</math>]] || <code>w[1]*(z) = exp(2*Pi*I*mu[1])*w[1]*(z*exp(- 2*Pi*I))+ C[1]*w[2]*(z)</code> || <code>Subscript[w, 1]*(z) == Exp[2*Pi*I*Subscript[\[Mu], 1]]*Subscript[w, 1]*(z*Exp[- 2*Pi*I])+ Subscript[C, 1]*Subscript[w, 2]*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7#Ex6 2.7#Ex6] || [[Item:Q909|<math>w_{2}(z) = e^{-2\pi i\mu_{2}}w_{2}(ze^{2\pi i})+C_{2}w_{1}(z)</math>]] || <code>w[2]*(z) = exp(- 2*Pi*I*mu[2])*w[2]*(z*exp(2*Pi*I))+ C[2]*w[1]*(z)</code> || <code>Subscript[w, 2]*(z) == Exp[- 2*Pi*I*Subscript[\[Mu], 2]]*Subscript[w, 2]*(z*Exp[2*Pi*I])+ Subscript[C, 2]*Subscript[w, 1]*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7#Ex7 2.7#Ex7] || [[Item:Q910|<math>\Lambda_{1} = -ie^{(\mu_{2}-\mu_{1})\pi i}C_{1}/(2\pi)</math>]] || <code>Lambda[1] = - I*exp((mu[2]- mu[1])* Pi*I)*C[1]/(2*Pi)</code> || <code>Subscript[\[CapitalLambda], 1] == - I*Exp[(Subscript[\[Mu], 2]- Subscript[\[Mu], 1])* Pi*I]*Subscript[C, 1]/(2*Pi)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7#Ex8 2.7#Ex8] || [[Item:Q911|<math>\Lambda_{2} = iC_{2}/(2\pi)</math>]] || <code>Lambda[2] = I*C[2]/(2*Pi)</code> || <code>Subscript[\[CapitalLambda], 2] == I*Subscript[C, 2]/(2*Pi)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7#Ex9 2.7#Ex9] || [[Item:Q912|<math>w = e^{-f_{0}z/2}W</math>]] || <code>w = exp(- f[0]*z/ 2)*W</code> || <code>w == Exp[- Subscript[f, 0]*z/ 2]*W</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7#Ex10 2.7#Ex10] || [[Item:Q913|<math>t = z^{1/2}</math>]] || <code>t = (z)^(1/ 2)</code> || <code>t == (z)^(1/ 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E21 2.7.E21] || [[Item:Q915|<math>w_{1}(x) = f^{-1/4}(x)\exp@{\int f^{1/2}(x)\diff{x}}\*\left(1+\epsilon_{1}(x)\right)</math>]] || <code>w[1]*(x) = (f)^(- 1/ 4)*(x)* exp(int((f)^(1/ 2)*(x), x))*(1 + epsilon[1]*(x))</code> || <code>Subscript[w, 1]*(x) == (f)^(- 1/ 4)*(x)* Exp[Integrate[(f)^(1/ 2)*(x), x, GenerateConditions->None]]*(1 + Subscript[\[Epsilon], 1]*(x))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-8.260557290-4.173606164*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 1}</code><br><code>-8.260557290-4.173606164*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 2}</code><br><code>-8.260557290-4.173606164*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I, epsilon = 3}</code><br><code>-10.30959540-3.624568058*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[1] = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2), epsilon = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-8.260557282600258, -4.173606160657738] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-8.260557282600258, -4.173606160657738] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E22 2.7.E22] || [[Item:Q916|<math>w_{2}(x) = f^{-1/4}(x)\exp@{-\int f^{1/2}(x)\diff{x}}\*\left(1+\epsilon_{2}(x)\right)</math>]] || <code>w[2]*(x) = (f)^(- 1/ 4)*(x)* exp(- int((f)^(1/ 2)*(x), x))*(1 + epsilon[2]*(x))</code> || <code>Subscript[w, 2]*(x) == (f)^(- 1/ 4)*(x)* Exp[- Integrate[(f)^(1/ 2)*(x), x, GenerateConditions->None]]*(1 + Subscript[\[Epsilon], 2]*(x))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.82331014e-1+.8803583156*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 1}</code><br><code>.82331014e-1+.8803583156*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 2}</code><br><code>.82331014e-1+.8803583156*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I, epsilon = 3}</code><br><code>-1.966707092+1.429396422*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, epsilon[2] = 1/2*3^(1/2)+1/2*I, w[2] = -1/2+1/2*I*3^(1/2), epsilon = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.08233101320006697, 0.8803583156922803] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 1], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.08233101320006697, 0.8803583156922803] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϵ, 2], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϵ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E31 2.7.E31] || [[Item:Q925|<math>\deriv[2]{w}{x} = (x+\ln@@{x})w</math>]] || <code>diff(w, [x$(2)]) = (x + ln(x))* w</code> || <code>D[w, {x, 2}] == (x + Log[x])* w</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[-1.650181190-.9527325540*I <- {w = 1/2*3^(1/2)+1/2*I, x = 1.5}</code><br><code>.1672703651+.9657359030e-1*I <- {w = 1/2*3^(1/2)+1/2*I, x = .5}</code><br><code>-2.332333875-1.346573590*I <- {w = 1/2*3^(1/2)+1/2*I, x = 2}</code><br><code>.9527325540-1.650181190*I <- {w = -1/2+1/2*I*3^(1/2), x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[-1.6501811896465322, -0.9527325540540821] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</code><br><code>Complex[0.1672703650342525, 0.09657359027997263] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E35 2.7.E35] || [[Item:Q929|<math>\ideriv[2]{w}{z} = w</math>]] || <code>diff(w, [z$(2)]) = w</code> || <code>D[w, {z, 2}] == w</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>70/70]: [[-.8660254040-.5000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.8660254040-.5000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>-.8660254040-.5000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>-.8660254040-.5000000000*I <- {w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[-0.8660254037844387, -0.49999999999999994] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.8660254037844387, -0.49999999999999994] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.7.E36 2.7.E36] || [[Item:Q930|<math>w(z) = Aw_{1}(z)+Bw_{2}(z)</math>]] || <code>w*(z) = A*w[1]*(z)+ B*w[2]*(z)</code> || <code>w*(z) == A*Subscript[w, 1]*(z)+ B*Subscript[w, 2]*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.7.E37 2.7.E37] || [[Item:Q931|<math>w(z) = Cw_{3}(z)+Dw_{4}(z)</math>]] || <code>w*(z) = C*w[3]*(z)+ D*w[4]*(z)</code> || <code>w*(z) == C*Subscript[w, 3]*(z)+ D*Subscript[w, 4]*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.8#Ex2 2.8#Ex2] || [[Item:Q937|<math>\xi = \int f^{1/2}(z)\diff{z}</math>]] || <code>xi = int((f)^(1/ 2)*(z), z)</code> || <code>\[Xi] == Integrate[(f)^(1/ 2)*(z), z, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-0.48296291314453416, -0.12940952255126037], Power[z, 2]]] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.4999999999999998, 0.8660254037844387], Times[Complex[-0.48296291314453416, -0.12940952255126037], Power[z, 2]]] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8#Ex4 2.8#Ex4] || [[Item:Q939|<math>\tfrac{2}{3}\xi^{3/2} = \int_{z_{0}}^{z}f^{1/2}(t)\diff{t}</math>]] || <code>(2)/(3)*(xi)^(3/ 2) = int((f)^(1/ 2)*(t), t = z[0]..z)</code> || <code>Divide[2,3]*\[Xi]^(3/ 2) == Integrate[(f)^(1/ 2)*(t), {t, Subscript[z, 0], z}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.4714045210+.4714045209*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = 1/2*3^(1/2)+1/2*I}</code><br><code>.2125854754-.4945213056*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = -1/2+1/2*I*3^(1/2)}</code><br><code>.2125854754-.4945213056*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = 1/2-1/2*I*3^(1/2)}</code><br><code>.4714045210+.4714045209*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.4714045207910317, 0.4714045207910316] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.21258547568851094, -0.4945213054980366] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8#Ex6 2.8#Ex6] || [[Item:Q941|<math>2\xi^{1/2} = \int_{z_{0}}^{z}f^{1/2}(t)\diff{t}</math>]] || <code>2*(xi)^(1/ 2) = int((f)^(1/ 2)*(t), t = z[0]..z)</code> || <code>2*\[Xi]^(1/ 2) == Integrate[(f)^(1/ 2)*(t), {t, Subscript[z, 0], z}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.931851653+.5176380902*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = 1/2*3^(1/2)+1/2*I}</code><br><code>1.673032607-.4482877363*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = -1/2+1/2*I*3^(1/2)}</code><br><code>1.673032607-.4482877363*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = 1/2-1/2*I*3^(1/2)}</code><br><code>1.931851653+.5176380902*I <- {f = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, z[0] = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.9318516525781366, 0.5176380902050415] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.6730326074756159, -0.4482877360840267] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E8 2.8.E8] || [[Item:Q942|<math>\ideriv[2]{W}{\xi} = \left(u^{2}\xi^{m}+\psi(\xi)\right)W</math>]] || <code>diff(W, [xi$(2)]) = ((u)^(2)* (xi)^(m)+ psi*(xi))* W</code> || <code>D[W, {\[Xi], 2}] == ((u)^(2)* \[Xi]^(m)+ \[Psi]*(\[Xi]))* W</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.4999999999-1.866025406*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, m = 1}</code><br><code>.8660254042-1.500000002*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, m = 2}</code><br><code>1.000000001-1.000000001*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, m = 3}</code><br><code>1.866025406+.4999999999*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2+1/2*I*3^(1/2), m = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [296 / 300]<div class="mw-collapsible-content"><code>{Complex[0.4999999999999997, -1.8660254037844388] <- {Rule[m, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8660254037844382, -1.5000000000000002] <- {Rule[m, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E9 2.8.E9] || [[Item:Q943|<math>\deriv[2]{W}{\xi} = \left(\frac{u^{2}}{\xi}+\frac{\rho}{\xi^{2}}\right)W</math>]] || <code>diff(W, [xi$(2)]) = (((u)^(2))/(xi)+(rho)/((xi)^(2)))* W</code> || <code>D[W, {\[Xi], 2}] == (Divide[(u)^(2),\[Xi]]+Divide[\[Rho],\[Xi]^(2)])* W</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-1.500000001-.8660254042*I <- {W = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I}</code><br><code>.1339745960+.5000000004*I <- {W = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2+1/2*I*3^(1/2)}</code><br><code>1.866025404-.5000000004*I <- {W = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2-1/2*I*3^(1/2)}</code><br><code>-.4999999996+.8660254040*I <- {W = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.5000000000000002, -0.8660254037844386] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.5000000000000004, -1.8660254037844388] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E10 2.8.E10] || [[Item:Q944|<math>\ideriv[2]{W}{\xi} = (u^{2}+\psi(\xi))W</math>]] || <code>diff(W, [xi$(2)]) = ((u)^(2)+ psi*(xi))* W</code> || <code>D[W, {\[Xi], 2}] == ((u)^(2)+ \[Psi]*(\[Xi]))* W</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [288 / 300]<div class="mw-collapsible-content"><code>288/300]: [[-.6467477718e-9-2.000000002*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I}</code><br><code>1.000000000-1.000000001*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2+1/2*I*3^(1/2)}</code><br><code>-1.000000001-1.000000000*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2-1/2*I*3^(1/2)}</code><br><code>.7500000002+.2990381054*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [288 / 300]<div class="mw-collapsible-content"><code>{Complex[0.0, -2.0] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.9999999999999998, -1.0000000000000002] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E14 2.8.E14] || [[Item:Q948|<math>\ideriv[2]{W}{\xi} = (u^{2}\xi+\psi(\xi))W</math>]] || <code>diff(W, [xi$(2)]) = ((u)^(2)* xi + psi*(xi))* W</code> || <code>D[W, {\[Xi], 2}] == ((u)^(2)* \[Xi]+ \[Psi]*(\[Xi]))* W</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.4999999999-1.866025406*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I}</code><br><code>1.866025406+.4999999999*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2+1/2*I*3^(1/2)}</code><br><code>-1.866025406-.4999999999*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2-1/2*I*3^(1/2)}</code><br><code>-.4999999999+1.866025406*I <- {W = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.4999999999999997, -1.8660254037844388] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.5, -0.8660254037844387] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E19 2.8.E19] || [[Item:Q953|<math>\AiryAi@{x} = \AiryBi@{x}</math>]] || <code>AiryAi(x) = AiryBi(x)</code> || <code>AiryAi[x] == AiryBi[x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>3/3]: [[-1.807192007 <- {x = 1.5}</code><br><code>-.6225834366 <- {x = .5}</code><br><code>-3.263170870 <- {x = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{-1.8071920067397889 <- {Rule[x, 1.5]}</code><br><code>-0.622583436622322 <- {Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.8.E24 2.8.E24] || [[Item:Q959|<math>\deriv[2]{W}{\xi} = \left(\frac{u^{2}}{4\xi}+\frac{\nu^{2}-1}{4\xi^{2}}+\frac{\psi(\xi)}{\xi}\right)W</math>]] || <code>diff(W, [xi$(2)]) = (((u)^(2))/(4*xi)+((nu)^(2)- 1)/(4*(xi)^(2))+(psi*(xi))/(xi))* W</code> || <code>D[W, {\[Xi], 2}] == (Divide[(u)^(2),4*\[Xi]]+Divide[\[Nu]^(2)- 1,4*\[Xi]^(2)]+Divide[\[Psi]*(\[Xi]),\[Xi]])* W</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.6250000006-1.332531755*I <- {W = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I}</code><br><code>-.7165063513-.4910254040*I <- {W = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2+1/2*I*3^(1/2)}</code><br><code>-.2834936493-.7410254042*I <- {W = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = 1/2-1/2*I*3^(1/2)}</code><br><code>-.3750000004-.8995190529*I <- {W = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, psi = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, xi = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.6250000000000002, -1.3325317547305482] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.7410254037844384, -0.9665063509461098] <- {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.9.E5 2.9.E5] || [[Item:Q978|<math>\rho^{2}+f_{0}\rho+g_{0} = 0</math>]] || <code>(rho)^(2)+ f[0]*rho + g[0] = 0</code> || <code>\[Rho]^(2)+ Subscript[f, 0]*\[Rho]+ Subscript[g, 0] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.9.E6 2.9.E6] || [[Item:Q979|<math>\alpha_{j} = (f_{1}\rho_{j}+g_{1})/(f_{0}\rho_{j}+2g_{0})</math>]] || <code>alpha[j] = (f[1]*rho[j]+ g[1])/(f[0]*rho[j]+ 2*g[0])</code> || <code>Subscript[\[Alpha], j] == (Subscript[f, 1]*Subscript[\[Rho], j]+ Subscript[g, 1])/(Subscript[f, 0]*Subscript[\[Rho], j]+ 2*Subscript[g, 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.9.E7 2.9.E7] || [[Item:Q980|<math>\rho_{j}(f_{0}+2\rho_{j})sa_{s,j} = \sum_{r=1}^{s}\left(\rho_{j}^{2}2^{r+1}\binom{\alpha_{j}+r-s}{r+1}+\rho_{j}\sum_{q=0}^{r+1}\binom{\alpha_{j}+r-s}{r+1-q}f_{q}+g_{r+1}\right)a_{s-r,j}</math>]] || <code>rho[j]*(f[0]+ 2*rho[j])* s*a[s , j] sum((rho(rho[j])^(2)*(2)^(r + 1)*binomial(alpha[j]+ r - s,r + 1)+ rho[j]*sum(binomial(alpha[j]+ r - s,r + 1 - q)*f[q], q = 0..r + 1)+ g[r + 1])* a[s - r , j], r = 1..s)</code> || <code>Subscript[\[Rho], j]*(Subscript[f, 0]+ 2*Subscript[\[Rho], j])* s*Subscript[a, s , j] Sum[(\[Rho](Subscript[\[Rho], j])^(2)*(2)^(r + 1)*Binomial[Subscript[\[Alpha], j]+ r - s,r + 1]+ Subscript[\[Rho], j]*Sum[Binomial[Subscript[\[Alpha], j]+ r - s,r + 1 - q]*Subscript[f, q], {q, 0, r + 1}, GenerateConditions->None]+ Subscript[g, r + 1])* Subscript[a, s - r , j], {r, 1, s}, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"></div></div>
|-
| [https://dlmf.nist.gov/2.9.E10 2.9.E10] || [[Item:Q983|<math>\sqrt{g_{0}}\kappa = \sqrt{2f_{0}f_{1}-4g_{1}}</math>]] || <code>sqrt(g[0])*kappa = sqrt(2*f[0]*f[1]- 4*g[1])</code> || <code>Sqrt[Subscript[g, 0]]*\[Kappa] == Sqrt[2*Subscript[f, 0]*Subscript[f, 1]- 4*Subscript[g, 1]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.9.E11 2.9.E11] || [[Item:Q984|<math>2g_{0}\alpha^{2}-(f_{0}f_{1}+2g_{0})\alpha+2g_{2}-f_{0}f_{2} = 0</math>]] || <code>2*g[0]*(alpha)^(2)-(f[0]*f[1]+ 2*g[0])* alpha + 2*g[2]- f[0]*f[2] = 0</code> || <code>2*Subscript[g, 0]*\[Alpha]^(2)-(Subscript[f, 0]*Subscript[f, 1]+ 2*Subscript[g, 0])* \[Alpha]+ 2*Subscript[g, 2]- Subscript[f, 0]*Subscript[f, 2] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.10.E3 2.10.E3] || [[Item:Q990|<math>S(n) = \sum_{j=1}^{n}j\ln@@{j}</math>]] || <code>S*(n) = sum(j*ln(j), j = 1..n)</code> || <code>S*(n) == Sum[j*Log[j], {j, 1, n}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[.8660254040+.5000000000*I <- {S = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.345756447+1.*I <- {S = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>-2.084055016+1.500000000*I <- {S = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>-.5000000000+.8660254040*I <- {S = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[n, 1], Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.34575644644898684, 0.9999999999999999] <- {Rule[n, 2], Rule[S, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.10.E4 2.10.E4] || [[Item:Q991|<math>S(n) = \tfrac{1}{2}n^{2}\ln@@{n}-\tfrac{1}{4}n^{2}+\tfrac{1}{2}n\ln@@{n}+\tfrac{1}{12}\ln@@{n}+C+\sum_{s=2}^{m-1}\frac{(-\BernoullinumberB{2s})}{2s(2s-1)(2s-2)}\frac{1}{n^{2s-2}}+R_{m}(n)</math>]] || <code>S*(n) = (1)/(2)*(n)^(2)* ln(n)-(1)/(4)*(n)^(2)+(1)/(2)*n*ln(n)+(1)/(12)*ln(n)+ C + sum((- bernoulli(2*s))/(2*s*(2*s - 1)*(2*s - 2))*(1)/((n)^(2*s - 2)), s = 2..m - 1)+ R[m]*(n)</code> || <code>S*(n) == Divide[1,2]*(n)^(2)* Log[n]-Divide[1,4]*(n)^(2)+Divide[1,2]*n*Log[n]+Divide[1,12]*Log[n]+ C + Sum[Divide[- BernoulliB[2*s],2*s*(2*s - 1)*(2*s - 2)]*Divide[1,(n)^(2*s - 2)], {s, 2, m - 1}, GenerateConditions->None]+ Subscript[R, m]*(n)</code> || Failure || Error || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/2.10.E6 2.10.E6] || [[Item:Q993|<math>C = \frac{\EulerConstant+\ln@{2\pi}}{12}-\frac{\Riemannzeta'@{2}}{2\pi^{2}}</math>]] || <code>C = (gamma + ln(2*Pi))/(12)-(subs( temp=2, diff( Zeta(temp), temp$(1) ) ))/(2*(Pi)^(2))</code> || <code>C == Divide[EulerGamma + Log[2*Pi],12]-Divide[D[Zeta[temp], {temp, 1}]/.temp-> 2,2*(Pi)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>10/10]: [[.6172709270+.5000000000*I <- {C = 1/2*3^(1/2)+1/2*I}</code><br><code>-.7487544770+.8660254040*I <- {C = -1/2+1/2*I*3^(1/2)}</code><br><code>.2512455230-.8660254040*I <- {C = 1/2-1/2*I*3^(1/2)}</code><br><code>-1.114779881-.5000000000*I <- {C = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>{Complex[0.6172709267506544, 0.49999999999999994] <- {Rule[C, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.748754477033784, 0.8660254037844387] <- {Rule[C, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.10.E6 2.10.E6] || [[Item:Q993|<math>\frac{\EulerConstant+\ln@{2\pi}}{12}-\frac{\Riemannzeta'@{2}}{2\pi^{2}} = \frac{1}{12}-\Riemannzeta'@{-1}</math>]] || <code>(gamma + ln(2*Pi))/(12)-(subs( temp=2, diff( Zeta(temp), temp$(1) ) ))/(2*(Pi)^(2)) = (1)/(12)- subs( temp=- 1, diff( Zeta(temp), temp$(1) ) )</code> || <code>Divide[EulerGamma + Log[2*Pi],12]-Divide[D[Zeta[temp], {temp, 1}]/.temp-> 2,2*(Pi)^(2)] == Divide[1,12]- (D[Zeta[temp], {temp, 1}]/.temp-> - 1)</code> || Failure || Successful || Successful [Tested: 0] || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/2.10.E9 2.10.E9] || [[Item:Q996|<math>\sum_{j=1}^{n-1}u_{j}v_{j} = U_{n-1}v_{n}+\sum_{j=1}^{n-1}U_{j}(v_{j}-v_{j+1})</math>]] || <code>sum(u[j]*v[j], j = 1..n - 1) = U[n - 1]*v[n]+ sum(U[j]*(v[j]- v[j + 1]), j = 1..n - 1)</code> || <code>Sum[Subscript[u, j]*Subscript[v, j], {j, 1, n - 1}, GenerateConditions->None] == Subscript[U, n - 1]*Subscript[v, n]+ Sum[Subscript[U, j]*(Subscript[v, j]- Subscript[v, j + 1]), {j, 1, n - 1}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.10.E11 2.10.E11] || [[Item:Q998|<math>S(\alpha,\beta,n) = \sum_{j=1}^{n-1}e^{ij\beta}j^{\alpha}</math>]] || <code>S*(alpha , beta , n) = sum(exp(I*j*beta)*(j)^(alpha), j = 1..n - 1)</code> || <code>S*(\[Alpha], \[Beta], n) == Sum[Exp[I*j*\[Beta]]*(j)^\[Alpha], {j, 1, n - 1}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.10.E12 2.10.E12] || [[Item:Q999|<math>|S(\alpha,\beta,n)| \leq \sum_{j=1}^{n-1}j^{\alpha}</math>]] || <code>abs(S*(alpha , beta , n)) <= sum((j)^(alpha), j = 1..n - 1)</code> || <code>Abs[S*(\[Alpha], \[Beta], n)] <= Sum[(j)^\[Alpha], {j, 1, n - 1}, GenerateConditions->None]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.10.E13 2.10.E13] || [[Item:Q1000|<math>U_{j} = e^{i\beta}(e^{ij\beta}-1)/(e^{i\beta}-1)</math>]] || <code>U[j] = exp(I*beta)*(exp(I*j*beta)- 1)/(exp(I*beta)- 1)</code> || <code>Subscript[U, j] == Exp[I*\[Beta]]*(Exp[I*j*\[Beta]]- 1)/(Exp[I*\[Beta]]- 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.10.E14 2.10.E14] || [[Item:Q1001|<math>S(\alpha,\beta,n) = \frac{e^{i\beta}}{e^{i\beta}-1}\left(e^{i(n-1)\beta}n^{\alpha}-1+\sum_{j=1}^{n-1}e^{ij\beta}\left(j^{\alpha}-(j+1)^{\alpha}\right)\right)</math>]] || <code>S*(alpha , beta , n) = (exp(I*beta))/(exp(I*beta)- 1)*(exp(I*(n - 1)* beta)*(n)^(alpha)- 1 + sum(exp(I*j*beta)*((j)^(alpha)-(j + 1)^(alpha)), j = 1..n - 1))</code> || <code>S*(\[Alpha], \[Beta], n) == Divide[Exp[I*\[Beta]],Exp[I*\[Beta]]- 1]*(Exp[I*(n - 1)* \[Beta]]*(n)^\[Alpha]- 1 + Sum[Exp[I*j*\[Beta]]*((j)^\[Alpha]-(j + 1)^\[Alpha]), {j, 1, n - 1}, GenerateConditions->None])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.10.E19 2.10.E19] || [[Item:Q1006|<math>\genhyperF{0}{2}@{-}{1,1}{x} = \sum_{j=0}^{\infty}\frac{x^{j}}{(j!)^{3}}</math>]] || <code>hypergeom([-], [1 , 1], x) = sum(((x)^(j))/((factorial(j))^(3)), j = 0..infinity)</code> || <code>HypergeometricPFQ[{-}, {1 , 1}, x] == Sum[Divide[(x)^(j),((j)!)^(3)], {j, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.10.E21 2.10.E21] || [[Item:Q1008|<math>\frac{\cot@{\pi t}}{2i} = -\frac{1}{2}-\frac{1}{e^{-2\pi it}-1}</math>]] || <code>(cot(Pi*t))/(2*I) = -(1)/(2)-(1)/(exp(- 2*Pi*I*t)- 1)</code> || <code>Divide[Cot[Pi*t],2*I] == -Divide[1,2]-Divide[1,Exp[- 2*Pi*I*t]- 1]</code> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 6]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[t, -2]}</code><br><code>Indeterminate <- {Rule[t, 2]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.10.E21 2.10.E21] || [[Item:Q1008|<math>-\frac{1}{2}-\frac{1}{e^{-2\pi it}-1} = \frac{1}{2}+\frac{1}{e^{2\pi it}-1}</math>]] || <code>-(1)/(2)-(1)/(exp(- 2*Pi*I*t)- 1) = (1)/(2)+(1)/(exp(2*Pi*I*t)- 1)</code> || <code>-Divide[1,2]-Divide[1,Exp[- 2*Pi*I*t]- 1] == Divide[1,2]+Divide[1,Exp[2*Pi*I*t]- 1]</code> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 6]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[t, -2]}</code><br><code>Indeterminate <- {Rule[t, 2]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.10.E23 2.10.E23] || [[Item:Q1010|<math>\genhyperF{0}{2}@{-}{1,1}{x} = \int_{-1/2}^{\infty}\frac{x^{t}}{(\EulerGamma@{t+1})^{3}}\diff{t}+2\realpart@@{\int_{-1/2}^{i\infty}\frac{x^{t}}{(\EulerGamma@{t+1})^{3}}\frac{\diff{t}}{e^{-2\pi it}-1}}</math>]] || <code>hypergeom([-], [1 , 1], x) = int(((x)^(t))/((GAMMA(t + 1))^(3)), t = - 1/ 2..infinity)+ 2*Re(int(((x)^(t))/((GAMMA(t + 1))^(3))*(1)/(exp(- 2*Pi*I*t)- 1), t = - 1/ 2..I*infinity))</code> || <code>HypergeometricPFQ[{-}, {1 , 1}, x] == Integrate[Divide[(x)^(t),(Gamma[t + 1])^(3)], {t, - 1/ 2, Infinity}, GenerateConditions->None]+ 2*Re[Integrate[Divide[(x)^(t),(Gamma[t + 1])^(3)]*Divide[1,Exp[- 2*Pi*I*t]- 1], {t, - 1/ 2, I*Infinity}, GenerateConditions->None]]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/2.10.E35 2.10.E35] || [[Item:Q1022|<math>g_{n} = \left(\frac{2}{\pi\sin@@{\alpha}}\right)^{1/2}\frac{\EulerGamma@{n+\frac{1}{2}}}{n!}\cos@{n\alpha+\tfrac{1}{2}\alpha-\tfrac{1}{4}\pi}</math>]] || <code>g[n] = ((2)/(Pi*sin(alpha)))^(1/ 2)*(GAMMA(n +(1)/(2)))/(factorial(n))*cos(n*alpha +(1)/(2)*alpha -(1)/(4)*Pi)</code> || <code>Subscript[g, n] == (Divide[2,Pi*Sin[\[Alpha]]])^(1/ 2)*Divide[Gamma[n +Divide[1,2]],(n)!]*Cos[n*\[Alpha]+Divide[1,2]*\[Alpha]-Divide[1,4]*Pi]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><code>90/90]: [[.7909815655+.5000000000*I <- {alpha = 1.5, g[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>1.388725754+.5000000000*I <- {alpha = 1.5, g[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.9745517365+.5000000000*I <- {alpha = 1.5, g[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>-.5750438385+.8660254040*I <- {alpha = 1.5, g[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><code>{Complex[0.7909815648537277, 0.49999999999999994] <- {Rule[n, 1], Rule[α, 1.5], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.3887257535176638, 0.49999999999999994] <- {Rule[n, 2], Rule[α, 1.5], Rule[Subscript[g, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.11.E1 2.11.E1] || [[Item:Q1024|<math>I(m) = \int_{0}^{\pi}\frac{\cos@{mt}}{t^{2}+1}\diff{t}</math>]] || <code>I*(m) = int((cos(m*t))/((t)^(2)+ 1), t = 0..Pi)</code> || <code>I*(m) == Integrate[Divide[Cos[m*t],(t)^(2)+ 1], {t, 0, Pi}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[2.012164326+2.811364624*I <- {I = 1/2*3^(1/2)+1/2*I, m = 1}</code><br><code>3.764776118+6.449767277*I <- {I = 1/2*3^(1/2)+1/2*I, m = 2}</code><br><code>10.44871992+12.82571836*I <- {I = 1/2*3^(1/2)+1/2*I, m = 3}</code><br><code>-.5451540752-.6604650959*I <- {I = -1/2+1/2*I*3^(1/2), m = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><code>{Complex[3.1301272053762923, 2.7021954356714506] <- {Rule[Complex[0, 1], 1], Rule[m, 1]}</code><br><code>Complex[7.946986696458338, 4.871470912282225] <- {Rule[Complex[0, 1], 1], Rule[m, 2]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/2.11#Ex1 2.11#Ex1] || [[Item:Q1026|<math>q_{1}(t) = -\frac{2t}{(t^{2}+1)^{2}}</math>]] || <code>q[1]*(t) = -(2*t)/(((t)^(2)+ 1)^(2))</code> || <code>Subscript[q, 1]*(t) == -Divide[2*t,((t)^(2)+ 1)^(2)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex2 2.11#Ex2] || [[Item:Q1027|<math>q_{2}(t) = \frac{24(t^{3}-t)}{(t^{2}+1)^{4}}</math>]] || <code>q[2]*(t) = (24*((t)^(3)- t))/(((t)^(2)+ 1)^(4))</code> || <code>Subscript[q, 2]*(t) == Divide[24*((t)^(3)- t),((t)^(2)+ 1)^(4)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex3 2.11#Ex3] || [[Item:Q1028|<math>q_{3}(t) = -\frac{240(3t^{5}-10t^{3}+3t)}{(t^{2}+1)^{6}}</math>]] || <code>q[3]*(t) = -(240*(3*(t)^(5)- 10*(t)^(3)+ 3*t))/(((t)^(2)+ 1)^(6))</code> || <code>Subscript[q, 3]*(t) == -Divide[240*(3*(t)^(5)- 10*(t)^(3)+ 3*t),((t)^(2)+ 1)^(6)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E5 2.11.E5] || [[Item:Q1030|<math>\genexpintE{p}@{z} = \frac{e^{-z}z^{p-1}}{\EulerGamma@{p}}\int_{0}^{\infty}\frac{e^{-zt}t^{p-1}}{1+t}\diff{t}</math>]] || <code>Ei(p, z) = (exp(- z)*(z)^(p - 1))/(GAMMA(p))*int((exp(- z*t)*(t)^(p - 1))/(1 + t), t = 0..infinity)</code> || <code>ExpIntegralE[p, z] == Divide[Exp[- z]*(z)^(p - 1),Gamma[p]]*Integrate[Divide[Exp[- z*t]*(t)^(p - 1),1 + t], {t, 0, Infinity}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 35]
|-
| [https://dlmf.nist.gov/2.11.E8 2.11.E8] || [[Item:Q1033|<math>n = \rho-p+\alpha</math>]] || <code>n = rho - p + alpha</code> || <code>n == \[Rho]- p + \[Alpha]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E9 2.11.E9] || [[Item:Q1034|<math>\frac{1}{1+t} = \sum_{s=0}^{n-1}(-1)^{s}t^{s}+(-1)^{n}\frac{t^{n}}{1+t}</math>]] || <code>(1)/(1 + t) = sum((- 1)^(s)* (t)^(s), s = 0..n - 1)+(- 1)^(n)*((t)^(n))/(1 + t)</code> || <code>Divide[1,1 + t] == Sum[(- 1)^(s)* (t)^(s), {s, 0, n - 1}, GenerateConditions->None]+(- 1)^(n)*Divide[(t)^(n),1 + t]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E11 2.11.E11] || [[Item:Q1036|<math>\frac{e^{-z}}{2\pi}\int_{0}^{\infty}\frac{e^{-zt}t^{n+p-1}}{1+t}\diff{t} = \frac{\EulerGamma@{n+p}}{2\pi}\frac{\genexpintE{n+p}@{z}}{z^{n+p-1}}</math>]] || <code>(exp(- z))/(2*Pi)*int((exp(- z*t)*(t)^(n + p - 1))/(1 + t), t = 0..infinity) = (GAMMA(n + p))/(2*Pi)*(Ei(n + p, z))/((z)^(n + p - 1))</code> || <code>Divide[Exp[- z],2*Pi]*Integrate[Divide[Exp[- z*t]*(t)^(n + p - 1),1 + t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[n + p],2*Pi]*Divide[ExpIntegralE[n + p, z],(z)^(n + p - 1)]</code> || Successful || Error || - || Successful [Tested: 189]
|-
| [https://dlmf.nist.gov/2.11.E14 2.11.E14] || [[Item:Q1039|<math>a_{2}(\theta,\alpha) = \frac{1}{12}(6\alpha^{2}-6\alpha+1)-\frac{\alpha}{1+e^{i\theta}}+\frac{1}{(1+e^{i\theta})^{2}}</math>]] || <code>a[2]*(theta , alpha) = (1)/(12)*(6*(alpha)^(2)- 6*alpha + 1)-(alpha)/(1 + exp(I*theta))+(1)/((1 + exp(I*theta))^(2))</code> || <code>Subscript[a, 2]*(\[Theta], \[Alpha]) == Divide[1,12]*(6*\[Alpha]^(2)- 6*\[Alpha]+ 1)-Divide[\[Alpha],1 + Exp[I*\[Theta]]]+Divide[1,(1 + Exp[I*\[Theta]])^(2)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E16 2.11.E16] || [[Item:Q1041|<math>c(\theta) = \sqrt{2(1+e^{i\theta}+i(\theta-\pi))}</math>]] || <code>c*(theta) = sqrt(2*(1 + exp(I*theta)+ I*(theta - Pi)))</code> || <code>c*(\[Theta]) == Sqrt[2*(1 + Exp[I*\[Theta]]+ I*(\[Theta]- Pi))]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E17 2.11.E17] || [[Item:Q1042|<math>h_{2s}(\theta,\alpha) = \frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}a_{2s}(\theta,\alpha)+(-1)^{s-1}i\frac{1\cdot 3\cdot 5\cdot\cdot\cdot(2s-1)}{(c(\theta))^{2s+1}}</math>]] || <code>h[2*s]*(theta , alpha) = (exp(I*alpha*(Pi - theta)))/(1 + exp(- I*theta))*a[2*s]*(theta , alpha)+(- 1)^(s - 1)* I*(1 * 3 * 5 * * *(2*s - 1))/((c*(theta))^(2*s + 1))</code> || <code>Subscript[h, 2*s]*(\[Theta], \[Alpha]) == Divide[Exp[I*\[Alpha]*(Pi - \[Theta])],1 + Exp[- I*\[Theta]]]*Subscript[a, 2*s]*(\[Theta], \[Alpha])+(- 1)^(s - 1)* I*Divide[1 * 3 * 5 * * *(2*s - 1),(c*(\[Theta]))^(2*s + 1)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E18 2.11.E18] || [[Item:Q1043|<math>h_{0}(\theta,\alpha) = \frac{e^{i\alpha(\pi-\theta)}}{1+e^{-i\theta}}-\frac{i}{c(\theta)}</math>]] || <code>h[0]*(theta , alpha) = (exp(I*alpha*(Pi - theta)))/(1 + exp(- I*theta))-(I)/(c*(theta))</code> || <code>Subscript[h, 0]*(\[Theta], \[Alpha]) == Divide[Exp[I*\[Alpha]*(Pi - \[Theta])],1 + Exp[- I*\[Theta]]]-Divide[I,c*(\[Theta])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E19 2.11.E19] || [[Item:Q1044|<math>w_{j}(z) = e^{\lambda_{j}z}z^{\mu_{j}}\sum_{s=0}^{n-1}\frac{a_{s,j}}{z^{s}}+R_{n}^{(j)}(z)</math>]] || <code>w[j]*(z) = exp(lambda[j]*z)*sum((a[s , j])/((z)^(s)), s = 0..n - 1)+ R(R[n])^(j)*(z)</code> || <code>Subscript[w, j]*(z) == Exp[Subscript[\[Lambda], j]*z]*Sum[Divide[Subscript[a, s , j],(z)^(s)], {s, 0, n - 1}, GenerateConditions->None]+ R(Subscript[R, n])^(j)*(z)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E26 2.11.E26] || [[Item:Q1051|<math>e^{5}\expintE@{5} = 0.17042\dots</math>]] || <code>exp(5)*Ei(5) = 0.17042</code> || <code>Exp[5]*ExpIntegralE[1, 5] == 0.17042</code> || Failure || Failure || Skip - No test values generated || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/2.11#Ex4 2.11#Ex4] || [[Item:Q1052|<math>\Delta^{0} = 0.00768</math>]] || <code>(Delta)^(0) = 0.00768</code> || <code>\[CapitalDelta]^(0) == 0.00768</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex5 2.11#Ex5] || [[Item:Q1053|<math>\Delta^{1} = 0.00154</math>]] || <code>(Delta)^(1) = 0.00154</code> || <code>\[CapitalDelta]^(1) == 0.00154</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex6 2.11#Ex6] || [[Item:Q1054|<math>\Delta^{2} = 0.00214</math>]] || <code>(Delta)^(2) = 0.00214</code> || <code>\[CapitalDelta]^(2) == 0.00214</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex7 2.11#Ex7] || [[Item:Q1055|<math>\Delta^{3} = 0.00192</math>]] || <code>(Delta)^(3) = 0.00192</code> || <code>\[CapitalDelta]^(3) == 0.00192</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex8 2.11#Ex8] || [[Item:Q1056|<math>\Delta^{4} = 0.00280</math>]] || <code>(Delta)^(4) = 0.00280</code> || <code>\[CapitalDelta]^(4) == 0.00280</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11#Ex9 2.11#Ex9] || [[Item:Q1057|<math>\Delta^{5} = 0.00434</math>]] || <code>(Delta)^(5) = 0.00434</code> || <code>\[CapitalDelta]^(5) == 0.00434</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E28 2.11.E28] || [[Item:Q1058|<math>0.00384-0.00038+0.00027-0.00012+0.00009-0.00007 = 0.00363</math>]] || <code>0.00384 - 0.00038 + 0.00027 - 0.00012 + 0.00009 - 0.00007 = 0.00363</code> || <code>0.00384 - 0.00038 + 0.00027 - 0.00012 + 0.00009 - 0.00007 == 0.00363</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E30 2.11.E30] || [[Item:Q1060|<math>a_{n} = \frac{e^{-z/2}}{z^{n-\kappa}n!}\left(\mu^{2}-(\kappa-\tfrac{1}{2})^{2}\right)\*\left(\mu^{2}-(\kappa-\tfrac{3}{2})^{2}\right)\*\cdot\cdot\cdot\left(\mu^{2}-(\kappa-n+\tfrac{1}{2})^{2}\right)</math>]] || <code>a[n] = (exp(- z/ 2))/((z)^(n - kappa)* factorial(n))*((mu)^(2)-(kappa -(1)/(2))^(2))*((mu)^(2)-(kappa -(3)/(2))^(2))* * * *((mu)^(2)-(kappa - n +(1)/(2))^(2))</code> || <code>Subscript[a, n] == Divide[Exp[- z/ 2],(z)^(n - \[Kappa])* (n)!]*(\[Mu]^(2)-(\[Kappa]-Divide[1,2])^(2))*(\[Mu]^(2)-(\[Kappa]-Divide[3,2])^(2))* * * *(\[Mu]^(2)-(\[Kappa]- n +Divide[1,2])^(2))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/2.11.E31 2.11.E31] || [[Item:Q1061|<math>\WhittakerconfhyperW{2.3}{0.5}@{1.0} = -0.83299\;50268\;27526\;\cdots</math>]] || <code>WhittakerW(2.3, 0.5, 1.0) = - 0.832995026827526</code> || <code>WhittakerW[2.3, 0.5, 1.0] == - 0.832995026827526</code> || Successful || Failure || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/2.11.E32 2.11.E32] || [[Item:Q1062|<math>d_{n} = \frac{\sum_{j=0}^{n}(-1)^{j}\binom{n}{j}(j+1)^{n-1}\frac{s_{j}}{a_{j+1}}}{\sum_{j=0}^{n}(-1)^{j}\binom{n}{j}(j+1)^{n-1}\frac{1}{a_{j+1}}}</math>]] || <code>d[n] = (sum((- 1)^(j)*binomial(n,j)*(j + 1)^(n - 1)*(s[j])/(a[j + 1]), j = 0..n))/(sum((- 1)^(j)*binomial(n,j)*(j + 1)^(n - 1)*(1)/(a[j + 1]), j = 0..n))</code> || <code>Subscript[d, n] == Divide[Sum[(- 1)^(j)*Binomial[n,j]*(j + 1)^(n - 1)*Divide[Subscript[s, j],Subscript[a, j + 1]], {j, 0, n}, GenerateConditions->None],Sum[(- 1)^(j)*Binomial[n,j]*(j + 1)^(n - 1)*Divide[1,Subscript[a, j + 1]], {j, 0, n}, GenerateConditions->None]]</code> || Failure || Failure || Error || Skipped - Because timed out
|-
|}

Latest revision as of 15:28, 25 May 2021

Areas
2.1 Definitions and Elementary Properties
2.2 Transcendental Equations
2.3 Integrals of a Real Variable
2.4 Contour Integrals
2.5 Mellin Transform Methods
2.6 Distributional Methods
2.7 Differential Equations
2.8 Differential Equations with a Parameter
2.9 Difference Equations
2.10 Sums and Sequences
2.11 Remainder Terms; Stokes Phenomenon
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