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JacobiCD






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCD[z,m] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/09.25.06.0005.01









  


  










Input Form





JacobiCD[z, m] \[Proportional] JacobiCD[Subscript[z, 0], m] + (-1 + m) JacobiND[Subscript[z, 0], m] JacobiSD[Subscript[z, 0], m] (z - Subscript[z, 0]) + ((m - 1)/2) JacobiCD[Subscript[z, 0], m] (JacobiND[Subscript[z, 0], m]^2 + m JacobiSD[Subscript[z, 0], m]^2) (z - Subscript[z, 0])^2 + (((-1 + m) JacobiSN[Subscript[z, 0], m])/ (6 JacobiDN[Subscript[z, 0], m]^4)) (4 m JacobiCN[Subscript[z, 0], m]^2 + (-1 + m) (1 + m JacobiSN[Subscript[z, 0], m]^2)) (z - Subscript[z, 0])^3 + (((-1 + m) JacobiCN[Subscript[z, 0], m])/ (24 JacobiDN[Subscript[z, 0], m]^5)) (4 m JacobiCN[Subscript[z, 0], m]^2 (1 + m JacobiSN[Subscript[z, 0], m]^2) + (-1 + m) (1 + m JacobiSN[Subscript[z, 0], m]^2 (14 + m JacobiSN[Subscript[z, 0], m]^2))) (z - Subscript[z, 0])^4 + (((-1 + m) JacobiSN[Subscript[z, 0], m])/ (120 JacobiDN[Subscript[z, 0], m]^6)) (16 m^2 JacobiCN[Subscript[z, 0], m]^4 + 44 (-1 + m) m JacobiCN[Subscript[z, 0], m]^2 (1 + m JacobiSN[Subscript[z, 0], m]^2) + (-1 + m)^2 (1 + m JacobiSN[Subscript[z, 0], m]^2 (14 + m JacobiSN[Subscript[z, 0], m]^2))) (z - Subscript[z, 0])^5 + \[Ellipsis] /; (z -> Subscript[z, 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





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