22.11: Difference between revisions

Latest revision as of 11:58, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
22.11.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} `\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiSN(z, k) = (2Pi)/(Kk)sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2n + 1)zeta))/(1 -(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiSN[z, (k)^2] == Divide[2Pi,Kk]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2n + 1)\[Zeta]],1 -(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} `\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiCN(z, k) = (2Pi)/(Kk)sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2n + 1)zeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiCN[z, (k)^2] == Divide[2Pi,Kk]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2n + 1)\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}} `\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiDN(z, k) = (Pi)/(2EllipticK(k))+(2Pi)/(EllipticK(k))sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(n)* cos(2nzeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n)), n = 1..infinity)	JacobiDN[z, (k)^2] == Divide[Pi,2EllipticK[(k)^2]]+Divide[2Pi,EllipticK[(k)^2]]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2n\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)], {n, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} `\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiCD(z, k) = (2Pi)/(Kk)sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(n +(1)/(2)) cos((2n + 1)zeta))/(1 -(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiCD[z, (k)^2] == Divide[2Pi,Kk]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2]) Cos[(2n + 1)\[Zeta]],1 -(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} `\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiSD(z, k) = (2Pi)/(Kksqrt(1 - (k)^(2)))sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2n + 1)zeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiSD[z, (k)^2] == Divide[2Pi,KkSqrt[1 - (k)^(2)]]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2n + 1)\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}} `\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiND(z, k) = (Pi)/(2EllipticK(k)sqrt(1 - (k)^(2)))+(2Pi)/(EllipticK(k)sqrt(1 - (k)^(2)))sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(n) cos(2nzeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n)), n = 1..infinity)	JacobiND[z, (k)^2] == Divide[Pi,2EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]+Divide[2Pi,EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n) Cos[2n\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)], {n, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} `\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiNS(z, k)-(Pi)/(2EllipticK(k))csc(zeta) = (2Pi)/(EllipticK(k))sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)* sin((2n + 1)zeta))/(1 -(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiNS[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]]Csc[\[Zeta]] == Divide[2Pi,EllipticK[(k)^2]]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)* Sin[(2n + 1)\[Zeta]],1 -(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} `\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiDS(z, k)-(Pi)/(2EllipticK(k))csc(zeta) = -(2Pi)/(EllipticK(k))sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)* sin((2n + 1)zeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiDS[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]]Csc[\[Zeta]] == -Divide[2Pi,EllipticK[(k)^2]]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)* Sin[(2n + 1)\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} `\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiCS(z, k)-(Pi)/(2EllipticK(k))cot(zeta) = -(2Pi)/(EllipticK(k))sum(((exp(- PiEllipticCK(k)/EllipticK(k)))^(2n)* sin(2nzeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n)), n = 1..infinity)	JacobiCS[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]]Cot[\[Zeta]] == -Divide[2Pi,EllipticK[(k)^2]]Sum[Divide[(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)* Sin[2n\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)], {n, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} `\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiDC(z, k)-(Pi)/(2EllipticK(k))sec(zeta) = (2Pi)/(EllipticK(k))sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1) cos((2n + 1)zeta))/(1 -(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiDC[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]]Sec[\[Zeta]] == Divide[2Pi,EllipticK[(k)^2]]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1) Cos[(2n + 1)\[Zeta]],1 -(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} `\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiNC(z, k)-(Pi)/(2EllipticK(k)sqrt(1 - (k)^(2)))sec(zeta) = -(2Pi)/(EllipticK(k)sqrt(1 - (k)^(2)))sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1) cos((2n + 1)zeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n + 1)), n = 0..infinity)	JacobiNC[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]Sec[\[Zeta]] == -Divide[2Pi,EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1) Cos[(2n + 1)\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n + 1)], {n, 0, Infinity}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} `\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	JacobiSC(z, k)-(Pi)/(2EllipticK(k)sqrt(1 - (k)^(2)))tan(zeta) = (2Pi)/(EllipticK(k)sqrt(1 - (k)^(2)))sum(((- 1)^(n)(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n) sin(2nzeta))/(1 +(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n)), n = 1..infinity)	JacobiSC[z, (k)^2]-Divide[Pi,2EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]Tan[\[Zeta]] == Divide[2Pi,EllipticK[(k)^2]Sqrt[1 - (k)^(2)]]Sum[Divide[(- 1)^(n)(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n) Sin[2n\[Zeta]],1 +(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)], {n, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
22.11.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}} `\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(JacobiSN(z, k))^(2) = (1)/((k)^(2))(1 -(EllipticE(k))/(EllipticK(k)))-(2(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))sum((n(q)^(n))/(1 -(exp(- PiEllipticCK(k)/EllipticK(k)))^(2n))cos(2n*zeta), n = 1..infinity)	(JacobiSN[z, (k)^2])^(2) == Divide[1,(k)^(2)](1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]Sum[Divide[n(q)^(n),1 -(Exp[- PiEllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2n)]Cos[2n*\[Zeta]], {n, 1, Infinity}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/22.11.E1 22.11.E1] || [[Item:Q7025|<math>\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E1 22.11.E1] || <math qid="Q7025">\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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-| [https://dlmf.nist.gov/22.11.E2 22.11.E2] || [[Item:Q7026|<math>\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E2 22.11.E2] || <math qid="Q7026">\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E3 22.11.E3] || [[Item:Q7027|<math>\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = (Pi)/(2*EllipticK(k))+(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]]+Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E3 22.11.E3] || <math qid="Q7027">\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = (Pi)/(2*EllipticK(k))+(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]]+Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E4 22.11.E4] || [[Item:Q7028|<math>\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(z, k) = (2*Pi)/(K*k)*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E4 22.11.E4] || <math qid="Q7028">\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(z, k) = (2*Pi)/(K*k)*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E5 22.11.E5] || [[Item:Q7029|<math>\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(z, k) = (2*Pi)/(K*k*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[z, (k)^2] == Divide[2*Pi,K*k*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E5 22.11.E5] || <math qid="Q7029">\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(z, k) = (2*Pi)/(K*k*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[z, (k)^2] == Divide[2*Pi,K*k*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E6 22.11.E6] || [[Item:Q7030|<math>\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(z, k) = (Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))+(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]+Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E6 22.11.E6] || <math qid="Q7030">\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(z, k) = (Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))+(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]+Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E7 22.11.E7] || [[Item:Q7031|<math>\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = (2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E7 22.11.E7] || <math qid="Q7031">\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = (2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E8 22.11.E8] || [[Item:Q7032|<math>\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E8 22.11.E8] || <math qid="Q7032">\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E9 22.11.E9] || [[Item:Q7033|<math>\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(z, k)-(Pi)/(2*EllipticK(k))*cot(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Cot[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E9 22.11.E9] || <math qid="Q7033">\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(z, k)-(Pi)/(2*EllipticK(k))*cot(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Cot[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E10 22.11.E10] || [[Item:Q7034|<math>\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(z, k)-(Pi)/(2*EllipticK(k))*sec(zeta) = (2*Pi)/(EllipticK(k))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Sec[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E10 22.11.E10] || <math qid="Q7034">\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(z, k)-(Pi)/(2*EllipticK(k))*sec(zeta) = (2*Pi)/(EllipticK(k))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Sec[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E11 22.11.E11] || [[Item:Q7035|<math>\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*sec(zeta) = -(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sec[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E11 22.11.E11] || <math qid="Q7035">\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*sec(zeta) = -(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sec[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E12 22.11.E12] || [[Item:Q7036|<math>\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*tan(zeta) = (2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Tan[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E12 22.11.E12] || <math qid="Q7036">\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*tan(zeta) = (2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Tan[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/22.11.E13 22.11.E13] || [[Item:Q7037|<math>\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2) = (1)/((k)^(2))*(1 -(EllipticE(k))/(EllipticK(k)))-(2*(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))*sum((n*(q)^(n))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n))*cos(2*n*zeta), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2) == Divide[1,(k)^(2)]*(1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2*(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]*Sum[Divide[n*(q)^(n),1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)]*Cos[2*n*\[Zeta]], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/22.11.E13 22.11.E13] || <math qid="Q7037">\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2) = (1)/((k)^(2))*(1 -(EllipticE(k))/(EllipticK(k)))-(2*(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))*sum((n*(q)^(n))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n))*cos(2*n*zeta), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2) == Divide[1,(k)^(2)]*(1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2*(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]*Sum[Divide[n*(q)^(n),1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)]*Cos[2*n*\[Zeta]], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
 |}
 </div>

22.11: Difference between revisions

Latest revision as of 11:58, 28 June 2021

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