13.29: Difference between revisions

Latest revision as of 11:35, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.29.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0} `\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	((x + yI)^(2)(n + mu -(1)/(2))((n + mu +(1)/(2))^(2)- (kappa)^(2)))/((n + mu)(n + mu +(1)/(2))(n + mu + 1))y(n + 1)+ 16((n + mu)^(2)-(1)/(2)kappa(x + yI)-(1)/(4))((x + yI)^(- n - mu -(1)/(2)) WhittakerM(kappa, n + mu, x + yI)); - 16((n + mu)^(2)-(1)/(4))y*(n - 1) = 0	Divide[(x + yI)^(2)(n + \[Mu]-Divide[1,2])((n + \[Mu]+Divide[1,2])^(2)- \[Kappa]^(2)),(n + \[Mu])(n + \[Mu]+Divide[1,2])(n + \[Mu]+ 1)]y(n + 1)+ 16((n + \[Mu])^(2)-Divide[1,2]\[Kappa](x + yI)-Divide[1,4])((x + yI)^(- n - \[Mu]-Divide[1,2]) WhittakerM[\[Kappa], n + \[Mu], x + yI])- 16((n + \[Mu])^(2)-Divide[1,4])y*(n - 1) == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.29.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)} `e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	exp(-(1)/(2)(x + y(I))) = sum((pochhammer(2mu, s)pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2mu, 2s)factorial(s))(-(x + y(I)))^(s) y(s), s = 0..infinity)	Exp[-Divide[1,2](x + y[I])] == Sum[Divide[Pochhammer[2\[Mu], s]Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2\[Mu], 2s](s)!](-(x + y[I]))^(s) y[s], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: .505394540e-1+.5994002652I Test Values: {kappa = 1/23^(1/2)+1/2I, mu = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2} Result: .7100232023-.2722368431I Test Values: {kappa = 1/23^(1/2)+1/2I, mu = 1/23^(1/2)+1/2I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.0505394539002913, 0.5994002653939074] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.9437946777348876, -0.07485124664222054] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.29.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0} `(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(n + a)w(n)-(2(n + a + 1)+ z - b)w(n + 1)+(n + a - b + 2)w(n + 2) = 0	(n + a)w[n]-(2(n + a + 1)+ z - b)w[n + 1]+(n + a - b + 2)w[n + 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.29.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}} `w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	w(n) = pochhammer(a, n)*KummerU(n + a, b, z)	w[n] == Pochhammer[a, n]*HypergeometricU[n + a, b, z]	Failure	Failure	Failed [300 / 300] Result: 3.350777422+.7382256467I Test Values: {a = -3/2, b = -3/2, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 1} Result: 1.327538097+1.034245119I Test Values: {a = -3/2, b = -3/2, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[3.3507774204902745, 0.7382256467588033] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.3275380963595516, 1.0342451193960447] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
13.29.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)} `z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(z)^(- a) = sum((pochhammer(a - b + 1, s))/(factorial(s))*w(s), s = 0..infinity)	(z)^(- a) == Sum[Divide[Pochhammer[a - b + 1, s],(s)!]*w[s], {s, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Failed [300 / 300] Result: Float(infinity)+Float(infinity)I Test Values: {a = -3/2, b = -3/2, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: Float(infinity)+Float(infinity)I Test Values: {a = -3/2, b = -3/2, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: DirectedInfinity[] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: DirectedInfinity[] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/13.29.E1 13.29.E1] || [[Item:Q4668|<math>\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((x + y*I)^(2)*(n + mu -(1)/(2))*((n + mu +(1)/(2))^(2)- (kappa)^(2)))/((n + mu)*(n + mu +(1)/(2))*(n + mu + 1))*y*(n + 1)+ 16*((n + mu)^(2)-(1)/(2)*kappa*(x + y*I)-(1)/(4))*((x + y*I)^(- n - mu -(1)/(2))* WhittakerM(kappa, n + mu, x + y*I))*; - 16*((n + mu)^(2)-(1)/(4))*y*(n - 1) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[(x + y*I)^(2)*(n + \[Mu]-Divide[1,2])*((n + \[Mu]+Divide[1,2])^(2)- \[Kappa]^(2)),(n + \[Mu])*(n + \[Mu]+Divide[1,2])*(n + \[Mu]+ 1)]*y*(n + 1)+ 16*((n + \[Mu])^(2)-Divide[1,2]*\[Kappa]*(x + y*I)-Divide[1,4])*((x + y*I)^(- n - \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], n + \[Mu], x + y*I])*- 16*((n + \[Mu])^(2)-Divide[1,4])*y*(n - 1) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/13.29.E1 13.29.E1] || <math qid="Q4668">\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{z^{2}(n+\mu-\tfrac{1}{2})\left((n+\mu+\tfrac{1}{2})^{2}-\kappa^{2}\right)}{(n+\mu)(n+\mu+\tfrac{1}{2})(n+\mu+1)}{y(n+1)}+16\left((n+\mu)^{2}-\tfrac{1}{2}\kappa z-\tfrac{1}{4}\right)y(n)\\ -16\left((n+\mu)^{2}-\tfrac{1}{4}\right)y(n-1) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((x + y*I)^(2)*(n + mu -(1)/(2))*((n + mu +(1)/(2))^(2)- (kappa)^(2)))/((n + mu)*(n + mu +(1)/(2))*(n + mu + 1))*y*(n + 1)+ 16*((n + mu)^(2)-(1)/(2)*kappa*(x + y*I)-(1)/(4))*((x + y*I)^(- n - mu -(1)/(2))* WhittakerM(kappa, n + mu, x + y*I))*; - 16*((n + mu)^(2)-(1)/(4))*y*(n - 1) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[(x + y*I)^(2)*(n + \[Mu]-Divide[1,2])*((n + \[Mu]+Divide[1,2])^(2)- \[Kappa]^(2)),(n + \[Mu])*(n + \[Mu]+Divide[1,2])*(n + \[Mu]+ 1)]*y*(n + 1)+ 16*((n + \[Mu])^(2)-Divide[1,2]*\[Kappa]*(x + y*I)-Divide[1,4])*((x + y*I)^(- n - \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], n + \[Mu], x + y*I])*- 16*((n + \[Mu])^(2)-Divide[1,4])*y*(n - 1) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/13.29.E3 13.29.E3] || [[Item:Q4670|<math>e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(-(1)/(2)*(x + y(I))) = sum((pochhammer(2*mu, s)*pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2*mu, 2*s)*factorial(s))*(-(x + y(I)))^(s)* y(s), s = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[-Divide[1,2]*(x + y[I])] == Sum[Divide[Pochhammer[2*\[Mu], s]*Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2*\[Mu], 2*s]*(s)!]*(-(x + y[I]))^(s)* y[s], {s, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .505394540e-1+.5994002652*I
+| [https://dlmf.nist.gov/13.29.E3 13.29.E3] || <math qid="Q4670">e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(-(1)/(2)*(x + y(I))) = sum((pochhammer(2*mu, s)*pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2*mu, 2*s)*factorial(s))*(-(x + y(I)))^(s)* y(s), s = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[-Divide[1,2]*(x + y[I])] == Sum[Divide[Pochhammer[2*\[Mu], s]*Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2*\[Mu], 2*s]*(s)!]*(-(x + y[I]))^(s)* y[s], {s, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .505394540e-1+.5994002652*I
 Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7100232023-.2722368431*I
 Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0505394539002913, 0.5994002653939074]
@@ Line 22: / Line 22: @@
 Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/13.29.E5 13.29.E5] || [[Item:Q4672|<math>(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(n + a)*w(n)-(2*(n + a + 1)+ z - b)*w(n + 1)+(n + a - b + 2)*w(n + 2) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(n + a)*w[n]-(2*(n + a + 1)+ z - b)*w[n + 1]+(n + a - b + 2)*w[n + 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/13.29.E5 13.29.E5] || <math qid="Q4672">(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(n+a)w(n)-\left(2(n+a+1)+z-b\right)w(n+1)+(n+a-b+2)w(n+2) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(n + a)*w(n)-(2*(n + a + 1)+ z - b)*w(n + 1)+(n + a - b + 2)*w(n + 2) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(n + a)*w[n]-(2*(n + a + 1)+ z - b)*w[n + 1]+(n + a - b + 2)*w[n + 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/13.29.E6 13.29.E6] || [[Item:Q4673|<math>w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(n) = pochhammer(a, n)*KummerU(n + a, b, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[n] == Pochhammer[a, n]*HypergeometricU[n + a, b, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.350777422+.7382256467*I
+| [https://dlmf.nist.gov/13.29.E6 13.29.E6] || <math qid="Q4673">w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(n) = pochhammer(a, n)*KummerU(n + a, b, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[n] == Pochhammer[a, n]*HypergeometricU[n + a, b, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.350777422+.7382256467*I
 Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.327538097+1.034245119*I
 Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.3507774204902745, 0.7382256467588033]
@@ Line 30: / Line 30: @@
 Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/13.29.E7 13.29.E7] || [[Item:Q4674|<math>z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(z)^(- a) = sum((pochhammer(a - b + 1, s))/(factorial(s))*w(s), s = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z)^(- a) == Sum[Divide[Pochhammer[a - b + 1, s],(s)!]*w[s], {s, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
+| [https://dlmf.nist.gov/13.29.E7 13.29.E7] || <math qid="Q4674">z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(z)^(- a) = sum((pochhammer(a - b + 1, s))/(factorial(s))*w(s), s = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z)^(- a) == Sum[Divide[Pochhammer[a - b + 1, s],(s)!]*w[s], {s, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {a = -3/2, b = -3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]

13.29: Difference between revisions

Latest revision as of 11:35, 28 June 2021

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