12.10: Difference between revisions

Latest revision as of 11:31, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
12.10#Ex1	${\displaystyle{\displaystyle a=+\tfrac{1}{2}\mu^{2}}}$ `a = +\tfrac{1}{2}\mu^{2}`	a = +(1)/(2)*(mu)^(2)	a == +Divide[1,2]*\[Mu]^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex2	${\displaystyle{\displaystyle x=\mu t\sqrt{2}}}$ `x = \mu t\sqrt{2}`	x = mutsqrt(2)	x == \[Mu]tSqrt[2]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10.E2	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}t}^{2}}=\mu^{4% }(t^{2}+1)w}}$ `\deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w`	diff(w, [t$(2)]) = (mu)^(4)((t)^(2)+ 1)w	D[w, {t, 2}] == \[Mu]^(4)((t)^(2)+ 1)w	Failure	Failure	Failed [300 / 300] Result: 2.814582564-1.625000003I Test Values: {mu = 1/23^(1/2)+1/2I, t = -3/2, w = 1/23^(1/2)+1/2I} Result: 1.625000003+2.814582564I Test Values: {mu = 1/23^(1/2)+1/2I, t = -3/2, w = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[2.814582562299425, -1.6250000000000009] Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.814582562299425, -1.6250000000000009] Test Values: {Rule[t, -1.5], Rule[w, 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
12.10.E2	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}t}^{2}}=\mu^{4% }(t^{2}-1)w}}$ `\deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w`	diff(w, [t$(2)]) = (mu)^(4)((t)^(2)- 1)w	D[w, {t, 2}] == \[Mu]^(4)((t)^(2)- 1)w	Failure	Failure	Failed [300 / 300] Result: 1.082531755-.6250000011I Test Values: {mu = 1/23^(1/2)+1/2I, t = -3/2, w = 1/23^(1/2)+1/2I} Result: .6250000011+1.082531755I Test Values: {mu = 1/23^(1/2)+1/2I, t = -3/2, w = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.0825317547305482, -0.6250000000000002] Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.0825317547305482, -0.6250000000000002] Test Values: {Rule[t, -1.5], Rule[w, 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
12.10.E13	${\displaystyle{\displaystyle v_{s}(t)=u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}% (t)}}$ `v_{s}(t) = u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}(t)`	v[s](t) = u[s](t)+(1)/(2)*tu[s - 1](t)- r[s - 2](t)	Subscript[v, s][t] == Subscript[u, s][t]+Divide[1,2]*Subscript[tu, s - 1][t]- Subscript[r, s - 2][t]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex9	${\displaystyle{\displaystyle\gamma_{0}=1}}$ `\gamma_{0} = 1`	gamma[0] = 1	Subscript[\[Gamma], 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex10	${\displaystyle{\displaystyle\gamma_{1}=-\tfrac{1}{24}}}$ `\gamma_{1} = -\tfrac{1}{24}`	gamma[1] = -(1)/(24)	Subscript[\[Gamma], 1] == -Divide[1,24]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex11	${\displaystyle{\displaystyle\gamma_{2}=\tfrac{1}{1152}}}$ `\gamma_{2} = \tfrac{1}{1152}`	gamma[2] = (1)/(1152)	Subscript[\[Gamma], 2] == Divide[1,1152]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex12	${\displaystyle{\displaystyle\gamma_{3}=\tfrac{1003}{4\;14720}}}$ `\gamma_{3} = \tfrac{1003}{4\;14720}`	gamma[3] = (1003)/(414720)	Subscript[\[Gamma], 3] == Divide[1003,414720]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex13	${\displaystyle{\displaystyle\gamma_{4}=-\tfrac{4027}{398\;13120}}}$ `\gamma_{4} = -\tfrac{4027}{398\;13120}`	gamma[4] = -(4027)/(39813120)	Subscript[\[Gamma], 4] == -Divide[4027,39813120]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex18	${\displaystyle{\displaystyle\mathsf{A}_{1}(\tau)=-\tfrac{1}{12}\tau(20\tau^{2}% +30\tau+9)}}$ `\mathsf{A}_{1}(\tau) = -\tfrac{1}{12}\tau(20\tau^{2}+30\tau+9)`	A[1](((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))) = -(1)/(12)((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))(20((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 30((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 9)	Subscript[A, 1]((Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == -Divide[1,12](Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))(20(Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 30(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 9)	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex19	${\displaystyle{\displaystyle\mathsf{A}_{2}(\tau)=\tfrac{1}{288}\tau^{2}(6160% \tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)}}$ `\mathsf{A}_{2}(\tau) = \tfrac{1}{288}\tau^{2}(6160\tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)`	A[2](((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))) = (1)/(288)((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))^(2)(6160((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))^(4)+ 18480((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))^(3)+ 19404((1)/(2)((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 8028((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 945)	Subscript[A, 2]((Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == Divide[1,288](Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)(6160(Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(4)+ 18480(Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(3)+ 19404(Divide[1,2](Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 8028(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 945)	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex22	${\displaystyle{\displaystyle A_{s}(\zeta)=\zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(% \phi(\zeta))^{6(2s-m)}u_{2s-m}(t)}}$ `A_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(\phi(\zeta))^{6(2s-m)}u_{2s-m}(t)`	A[s](zeta) = (zeta)^(- 3s) sum((-(6m + 1)/(6m - 1)alpha[m])((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6(2s - m))* u[2s - m](t), m = 0..2s)	Subscript[A, s][\[Zeta]] == \[Zeta]^(- 3s) Sum[(-Divide[6m + 1,6m - 1]Subscript[\[Alpha], m])(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6(2s - m))* Subscript[u, 2s - m][t], {m, 0, 2s}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex23	${\displaystyle{\displaystyle\zeta^{2}B_{s}(\zeta)=-\zeta^{-3s}\sum_{m=0}^{2s+1% }\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)}}$ `\zeta^{2}B_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)`	(zeta)^(2)* B[s](zeta) = - (zeta)^(- 3s) sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6(2s - m + 1))* u[2s - m + 1](t), m = 0..2s + 1)	\[Zeta]^(2)* Subscript[B, s][\[Zeta]] == - \[Zeta]^(- 3s) Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6(2s - m + 1))* Subscript[u, 2s - m + 1][t], {m, 0, 2s + 1}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex28	${\displaystyle{\displaystyle\zeta C_{s}(\zeta)=-\zeta^{-3s}\sum_{m=0}^{2s+1}% \beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)}}$ `\zeta C_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)`	zetaC[s](zeta) = - (zeta)^(- 3s)* sum((-(6m + 1)/(6m - 1)alpha[m])((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6(2s - m + 1))* v[2s - m + 1](t), m = 0..2s + 1)	\[Zeta]Subscript[C, s][\[Zeta]] == - \[Zeta]^(- 3s)* Sum[(-Divide[6m + 1,6m - 1]Subscript[\[Alpha], m])(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6(2s - m + 1))* Subscript[v, 2s - m + 1][t], {m, 0, 2s + 1}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
12.10#Ex29	${\displaystyle{\displaystyle D_{s}(\zeta)=\zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}% (\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)}}$ `D_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}(\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)`	D[s](zeta) = (zeta)^(- 3s) sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6(2s - m))* v[2s - m](t), m = 0..2s)	Subscript[D, s][\[Zeta]] == \[Zeta]^(- 3s) Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6(2s - m))* Subscript[v, 2s - m][t], {m, 0, 2s}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex1 12.10#Ex1] || [[Item:Q4154|<math>a = +\tfrac{1}{2}\mu^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = +\tfrac{1}{2}\mu^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = +(1)/(2)*(mu)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == +Divide[1,2]*\[Mu]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex1 12.10#Ex1] || <math qid="Q4154">a = +\tfrac{1}{2}\mu^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = +\tfrac{1}{2}\mu^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = +(1)/(2)*(mu)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == +Divide[1,2]*\[Mu]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex2 12.10#Ex2] || [[Item:Q4155|<math>x = \mu t\sqrt{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = \mu t\sqrt{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = mu*t*sqrt(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == \[Mu]*t*Sqrt[2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex2 12.10#Ex2] || <math qid="Q4155">x = \mu t\sqrt{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x = \mu t\sqrt{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x = mu*t*sqrt(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x == \[Mu]*t*Sqrt[2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/12.10.E2 12.10.E2] || [[Item:Q4156|<math>\deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [t$(2)]) = (mu)^(4)*((t)^(2)+ 1)*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {t, 2}] == \[Mu]^(4)*((t)^(2)+ 1)*w</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.814582564-1.625000003*I
+| [https://dlmf.nist.gov/12.10.E2 12.10.E2] || <math qid="Q4156">\deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [t$(2)]) = (mu)^(4)*((t)^(2)+ 1)*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {t, 2}] == \[Mu]^(4)*((t)^(2)+ 1)*w</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.814582564-1.625000003*I
 Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.625000003+2.814582564*I
 Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = -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: Complex[2.814582562299425, -1.6250000000000009]
@@ Line 24: / Line 24: @@
 Test Values: {Rule[t, -1.5], Rule[w, 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>
 |-
-| [https://dlmf.nist.gov/12.10.E2 12.10.E2] || [[Item:Q4156|<math>\deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [t$(2)]) = (mu)^(4)*((t)^(2)- 1)*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {t, 2}] == \[Mu]^(4)*((t)^(2)- 1)*w</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.082531755-.6250000011*I
+| [https://dlmf.nist.gov/12.10.E2 12.10.E2] || <math qid="Q4156">\deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [t$(2)]) = (mu)^(4)*((t)^(2)- 1)*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {t, 2}] == \[Mu]^(4)*((t)^(2)- 1)*w</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.082531755-.6250000011*I
 Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6250000011+1.082531755*I
 Test Values: {mu = 1/2*3^(1/2)+1/2*I, t = -3/2, w = -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: Complex[1.0825317547305482, -0.6250000000000002]
@@ Line 30: / Line 30: @@
 Test Values: {Rule[t, -1.5], Rule[w, 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/12.10.E13 12.10.E13] || [[Item:Q4171|<math>v_{s}(t) = u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>v_{s}(t) = u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v[s](t) = u[s](t)+(1)/(2)*tu[s - 1](t)- r[s - 2](t)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[v, s][t] == Subscript[u, s][t]+Divide[1,2]*Subscript[tu, s - 1][t]- Subscript[r, s - 2][t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10.E13 12.10.E13] || <math qid="Q4171">v_{s}(t) = u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>v_{s}(t) = u_{s}(t)+\tfrac{1}{2}tu_{s-1}(t)-r_{s-2}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v[s](t) = u[s](t)+(1)/(2)*tu[s - 1](t)- r[s - 2](t)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[v, s][t] == Subscript[u, s][t]+Divide[1,2]*Subscript[tu, s - 1][t]- Subscript[r, s - 2][t]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex9 12.10#Ex9] || [[Item:Q4175|<math>\gamma_{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex9 12.10#Ex9] || <math qid="Q4175">\gamma_{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{0} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[0] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex10 12.10#Ex10] || [[Item:Q4176|<math>\gamma_{1} = -\tfrac{1}{24}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{1} = -\tfrac{1}{24}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[1] = -(1)/(24)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 1] == -Divide[1,24]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex10 12.10#Ex10] || <math qid="Q4176">\gamma_{1} = -\tfrac{1}{24}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{1} = -\tfrac{1}{24}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[1] = -(1)/(24)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 1] == -Divide[1,24]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex11 12.10#Ex11] || [[Item:Q4177|<math>\gamma_{2} = \tfrac{1}{1152}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{2} = \tfrac{1}{1152}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[2] = (1)/(1152)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 2] == Divide[1,1152]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex11 12.10#Ex11] || <math qid="Q4177">\gamma_{2} = \tfrac{1}{1152}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{2} = \tfrac{1}{1152}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[2] = (1)/(1152)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 2] == Divide[1,1152]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex12 12.10#Ex12] || [[Item:Q4178|<math>\gamma_{3} = \tfrac{1003}{4\;14720}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{3} = \tfrac{1003}{4\;14720}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[3] = (1003)/(414720)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 3] == Divide[1003,414720]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex12 12.10#Ex12] || <math qid="Q4178">\gamma_{3} = \tfrac{1003}{4\;14720}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{3} = \tfrac{1003}{4\;14720}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[3] = (1003)/(414720)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 3] == Divide[1003,414720]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex13 12.10#Ex13] || [[Item:Q4179|<math>\gamma_{4} = -\tfrac{4027}{398\;13120}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{4} = -\tfrac{4027}{398\;13120}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[4] = -(4027)/(39813120)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 4] == -Divide[4027,39813120]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex13 12.10#Ex13] || <math qid="Q4179">\gamma_{4} = -\tfrac{4027}{398\;13120}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{4} = -\tfrac{4027}{398\;13120}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[4] = -(4027)/(39813120)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 4] == -Divide[4027,39813120]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex18 12.10#Ex18] || [[Item:Q4198|<math>\mathsf{A}_{1}(\tau) = -\tfrac{1}{12}\tau(20\tau^{2}+30\tau+9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathsf{A}_{1}(\tau) = -\tfrac{1}{12}\tau(20\tau^{2}+30\tau+9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1]*(((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))) = -(1)/(12)*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))*(20*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 30*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1]*((Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == -Divide[1,12]*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))*(20*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 30*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex18 12.10#Ex18] || <math qid="Q4198">\mathsf{A}_{1}(\tau) = -\tfrac{1}{12}\tau(20\tau^{2}+30\tau+9)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathsf{A}_{1}(\tau) = -\tfrac{1}{12}\tau(20\tau^{2}+30\tau+9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1]*(((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))) = -(1)/(12)*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))*(20*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 30*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1]*((Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == -Divide[1,12]*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))*(20*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 30*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex19 12.10#Ex19] || [[Item:Q4199|<math>\mathsf{A}_{2}(\tau) = \tfrac{1}{288}\tau^{2}(6160\tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathsf{A}_{2}(\tau) = \tfrac{1}{288}\tau^{2}(6160\tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2]*(((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))) = (1)/(288)*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)*(6160*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(4)+ 18480*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(3)+ 19404*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 8028*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 945)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2]*((Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == Divide[1,288]*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)*(6160*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(4)+ 18480*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(3)+ 19404*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 8028*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 945)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex19 12.10#Ex19] || <math qid="Q4199">\mathsf{A}_{2}(\tau) = \tfrac{1}{288}\tau^{2}(6160\tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathsf{A}_{2}(\tau) = \tfrac{1}{288}\tau^{2}(6160\tau^{4}+18480\tau^{3}+19404\tau^{2}+8028\tau+945)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2]*(((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))) = (1)/(288)*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)*(6160*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(4)+ 18480*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(3)+ 19404*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))^(2)+ 8028*((1)/(2)*((t)/(sqrt((t)^(2)- 1))- 1))+ 945)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2]*((Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))) == Divide[1,288]*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)*(6160*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(4)+ 18480*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(3)+ 19404*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))^(2)+ 8028*(Divide[1,2]*(Divide[t,Sqrt[(t)^(2)- 1]]- 1))+ 945)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex22 12.10#Ex22] || [[Item:Q4208|<math>A_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(\phi(\zeta))^{6(2s-m)}u_{2s-m}(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(\phi(\zeta))^{6(2s-m)}u_{2s-m}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[s](zeta) = (zeta)^(- 3*s)* sum((-(6*m + 1)/(6*m - 1)*alpha[m])*((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6*(2*s - m))* u[2*s - m](t), m = 0..2*s)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, s][\[Zeta]] == \[Zeta]^(- 3*s)* Sum[(-Divide[6*m + 1,6*m - 1]*Subscript[\[Alpha], m])*(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6*(2*s - m))* Subscript[u, 2*s - m][t], {m, 0, 2*s}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex22 12.10#Ex22] || <math qid="Q4208">A_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(\phi(\zeta))^{6(2s-m)}u_{2s-m}(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\beta_{m}(\phi(\zeta))^{6(2s-m)}u_{2s-m}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[s](zeta) = (zeta)^(- 3*s)* sum((-(6*m + 1)/(6*m - 1)*alpha[m])*((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6*(2*s - m))* u[2*s - m](t), m = 0..2*s)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, s][\[Zeta]] == \[Zeta]^(- 3*s)* Sum[(-Divide[6*m + 1,6*m - 1]*Subscript[\[Alpha], m])*(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6*(2*s - m))* Subscript[u, 2*s - m][t], {m, 0, 2*s}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex23 12.10#Ex23] || [[Item:Q4209|<math>\zeta^{2}B_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta^{2}B_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(zeta)^(2)* B[s](zeta) = - (zeta)^(- 3*s)* sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6*(2*s - m + 1))* u[2*s - m + 1](t), m = 0..2*s + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta]^(2)* Subscript[B, s][\[Zeta]] == - \[Zeta]^(- 3*s)* Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6*(2*s - m + 1))* Subscript[u, 2*s - m + 1][t], {m, 0, 2*s + 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex23 12.10#Ex23] || <math qid="Q4209">\zeta^{2}B_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta^{2}B_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\alpha_{m}(\phi(\zeta))^{6(2s-m+1)}u_{2s-m+1}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(zeta)^(2)* B[s](zeta) = - (zeta)^(- 3*s)* sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6*(2*s - m + 1))* u[2*s - m + 1](t), m = 0..2*s + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta]^(2)* Subscript[B, s][\[Zeta]] == - \[Zeta]^(- 3*s)* Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6*(2*s - m + 1))* Subscript[u, 2*s - m + 1][t], {m, 0, 2*s + 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex28 12.10#Ex28] || [[Item:Q4215|<math>\zeta C_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta C_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta*C[s](zeta) = - (zeta)^(- 3*s)* sum((-(6*m + 1)/(6*m - 1)*alpha[m])*((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6*(2*s - m + 1))* v[2*s - m + 1](t), m = 0..2*s + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta]*Subscript[C, s][\[Zeta]] == - \[Zeta]^(- 3*s)* Sum[(-Divide[6*m + 1,6*m - 1]*Subscript[\[Alpha], m])*(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6*(2*s - m + 1))* Subscript[v, 2*s - m + 1][t], {m, 0, 2*s + 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex28 12.10#Ex28] || <math qid="Q4215">\zeta C_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta C_{s}(\zeta) = -\zeta^{-3s}\sum_{m=0}^{2s+1}\beta_{m}(\phi(\zeta))^{6(2s-m+1)}v_{2s-m+1}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta*C[s](zeta) = - (zeta)^(- 3*s)* sum((-(6*m + 1)/(6*m - 1)*alpha[m])*((((zeta)/((t)^(2)- 1))^((1)/(4))))^(6*(2*s - m + 1))* v[2*s - m + 1](t), m = 0..2*s + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta]*Subscript[C, s][\[Zeta]] == - \[Zeta]^(- 3*s)* Sum[(-Divide[6*m + 1,6*m - 1]*Subscript[\[Alpha], m])*(((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4])))^(6*(2*s - m + 1))* Subscript[v, 2*s - m + 1][t], {m, 0, 2*s + 1}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/12.10#Ex29 12.10#Ex29] || [[Item:Q4216|<math>D_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}(\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}(\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[s](zeta) = (zeta)^(- 3*s)* sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6*(2*s - m))* v[2*s - m](t), m = 0..2*s)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, s][\[Zeta]] == \[Zeta]^(- 3*s)* Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6*(2*s - m))* Subscript[v, 2*s - m][t], {m, 0, 2*s}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/12.10#Ex29 12.10#Ex29] || <math qid="Q4216">D_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}(\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{s}(\zeta) = \zeta^{-3s}\sum_{m=0}^{2s}\alpha_{m}(\phi(\zeta))^{6(2s-m)}v_{2s-m}(t)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[s](zeta) = (zeta)^(- 3*s)* sum((alpha[m]((((zeta)/((t)^(2)- 1))^((1)/(4)))))^(6*(2*s - m))* v[2*s - m](t), m = 0..2*s)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, s][\[Zeta]] == \[Zeta]^(- 3*s)* Sum[(Subscript[\[Alpha], m][((Divide[\[Zeta],(t)^(2)- 1])^(Divide[1,4]))])^(6*(2*s - m))* Subscript[v, 2*s - m][t], {m, 0, 2*s}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |}
 </div>

12.10: Difference between revisions

Latest revision as of 11:31, 28 June 2021

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