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JacobiZeta




Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/08.07.06.0005.01









  


  








Input Form





JacobiZeta[z, m] == (1 - (2 z)/Pi) EllipticE[m] - Cos[z] Sum[(Pochhammer[-(1/2), k]/k!) Hypergeometric2F1[1/2, 1/2 - k, 3/2, Cos[z]^2] m^k, {k, 0, Infinity}] - (EllipticE[m]/EllipticK[m]) Sum[((-1)^k/k) Binomial[k - 1/2, k] Hypergeometric2F1[k + 1/2, k + 1/2, 2 k + 1, m] Sin[2 k z] (m/4)^k, {k, 1, Infinity}]








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