D[JacobiNS[z, m], {m, 2}] == (1/(4 (-1 + m)^2 m^2)) (2 (-1 + m) JacobiCS[z, m] JacobiDS[z, m] ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiCD[z, m] JacobiSN[z, m]) + 2 m JacobiCS[z, m] JacobiDS[z, m] ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiCD[z, m] JacobiSN[z, m]) + JacobiCS[z, m]^2 JacobiNS[z, m] ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiDN[z, m] JacobiSC[z, m]) ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiCD[z, m] JacobiSN[z, m]) + JacobiDS[z, m]^2 JacobiNS[z, m] ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiCD[z, m] JacobiSN[z, m])^2 + (1 - m) m JacobiCS[z, m] JacobiDS[z, m] (2 z + (1/m) (EllipticE[JacobiAmplitude[z, m], m] - EllipticF[JacobiAmplitude[z, m], m]) - 2 JacobiCD[z, m] JacobiSN[z, m] - ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) JacobiND[z, m] JacobiSD[z, m] JacobiSN[z, m] + (1/(-1 + m)) (JacobiCD[z, m] JacobiCN[z, m] JacobiDN[z, m] (z - m z - EllipticE[JacobiAmplitude[z, m], m] + m JacobiCD[z, m] JacobiSN[z, m])) + (1/((-1 + m) m)) ((((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) JacobiDN[z, m] - m JacobiCN[z, m] JacobiSN[z, m]) Sqrt[1 - m JacobiSN[z, m]^2])))

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z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> ds </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> cd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cs </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> ds </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mrow> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> am </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> 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2001-10-29