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JacobiAmplitude






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiAmplitude[z,m] > Series representations > Generalized power series > Expansions at generic point m==m0 > For the function itself





http://functions.wolfram.com/09.24.06.0010.01









  


  










Input Form





JacobiAmplitude[z, m] \[Proportional] JacobiAmplitude[z, Subscript[m, 0]] + (1/(2 (-1 + Subscript[m, 0]) Subscript[m, 0])) (((-1 + Subscript[m, 0]) z + EllipticE[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]]) JacobiDN[z, Subscript[m, 0]] - Subscript[m, 0] JacobiCN[z, Subscript[m, 0]] JacobiSN[z, Subscript[m, 0]]) (m - Subscript[m, 0]) - (1/(8 (-1 + Subscript[m, 0])^2 Subscript[m, 0]^2)) ((-((-1 + Subscript[m, 0]) z + EllipticE[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]])) JacobiDN[z, Subscript[m, 0]]^2 Sqrt[1 - Subscript[m, 0] JacobiSN[z, Subscript[m, 0]]^2] + Subscript[m, 0] JacobiCN[z, Subscript[m, 0]] JacobiSN[z, Subscript[m, 0]] (-2 Subscript[m, 0] + (-1 + Subscript[m, 0])^2 z^2 + EllipticE[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]] (2 (-1 + Subscript[m, 0]) z + EllipticE[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]]) - Subscript[m, 0] JacobiCN[z, Subscript[m, 0]]^2 + Subscript[m, 0] JacobiSN[z, Subscript[m, 0]]^2) + JacobiDN[z, Subscript[m, 0]] (EllipticE[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]] (-1 + 3 Subscript[m, 0] + Subscript[m, 0] JacobiCN[z, Subscript[m, 0]]^2 - 2 Subscript[m, 0] JacobiSN[z, Subscript[m, 0]]^2) + Subscript[m, 0] JacobiCN[z, Subscript[m, 0]] JacobiSN[z, Subscript[m, 0]] Sqrt[1 - Subscript[m, 0] JacobiSN[z, Subscript[m, 0]]^2] + (-1 + Subscript[m, 0]) (2 (-1 + Subscript[m, 0]) z + EllipticF[JacobiAmplitude[z, Subscript[m, 0]], Subscript[m, 0]] + Subscript[m, 0] z (JacobiCN[z, Subscript[m, 0]]^2 - 2 JacobiSN[z, Subscript[m, 0]]^2)))) (m - Subscript[m, 0])^2 + \[Ellipsis] /; (m -> Subscript[m, 0])










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)





2007-05-02