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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/08.07.06.0036.01









  


  










Input Form





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





2007-05-02





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