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JacobiDS






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDS[z,m] > Differentiation > Low-order differentiation > With respect to m





http://functions.wolfram.com/09.30.20.0004.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998- Wolfram Research, Inc.