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JacobiNC






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiNC[z,m] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/09.31.16.0015.01









  


  










Input Form





JacobiNC[z/M + K/(n M), l] == (-(M/Sqrt[1 - l])) (JacobiNS[z, m]/JacobiNC[z, m]) Product[(1 - m JacobiSN[(2 r - 1) (EllipticK[m]/n), m]^2 JacobiSN[z, m]^2)/ (1 - JacobiSN[z, m]^2/JacobiSN[2 r (EllipticK[m]/n), m]^2), {r, 1, n/2}] /; Element[n/2, Integers] && n > 0 && l == m^n Product[JacobiSN[((2 r - 1) EllipticK[m])/n, m]^8, {r, 1, n/2}] && M == Product[JacobiSN[((2 r - 1) EllipticK[m])/n, m]^2/ JacobiSN[(2 r EllipticK[m])/n, m]^2, {r, 1, n/2}]










Standard Form





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MathML Form







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</mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> n </mi> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 8 </mn> </msup> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> M </mi> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> r </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> </munderover> <mfrac> <msup> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mi> n </mi> </mfrac> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <msup> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> r </mi> <mo> &#8290; 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Rule Form





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2001-10-29





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