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JacobiZeta






Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Series representations > Generalized power series > Expansions at z==Pi/2+Pi u/;uZ && m>1





http://functions.wolfram.com/08.07.06.0028.01









  


  










Input Form





JacobiZeta[z, m] \[Proportional] (-JacobiZeta[ArcCsc[Sqrt[m]], m]) (I Sqrt[-(1/(z - Subscript[z, 0])^2)] (z - Subscript[z, 0]) + Sqrt[(z - Subscript[z, 0])^2]/(z - Subscript[z, 0])) + (Sqrt[1 - m] - EllipticE[m]/(Sqrt[1 - m] EllipticK[m])) (z - Subscript[z, 0]) + (m/(6 Sqrt[1 - m]) + (m EllipticE[m])/ (6 (1 - m)^(3/2) EllipticK[m])) (z - Subscript[z, 0])^3 + (((-4 + m) m)/(120 (1 - m)^(3/2)) - (m (4 + 5 m) EllipticE[m])/ (120 (1 - m)^(5/2) EllipticK[m])) (z - Subscript[z, 0])^5 + \[Ellipsis] /; (z -> Subscript[z, 0]) && Subscript[z, 0] == Pi/2 + Pi u && Element[u, Integers] && Element[m, Reals] && m > 1










Standard Form





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MathML Form







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<semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> JacobiZeta </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#918; </ci> </apply> <apply> <ci> VerticalSeparator </ci> <apply> <arccsc /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> 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Rule Form





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2007-05-02





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