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JacobiZeta






Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Series representations > Generalized power series > Expansions on branch cuts > Formulas on real axis for real m > For m>1,Pi(u+1/2)<xu+1)-csc-1(m1/2)/;uZ





http://functions.wolfram.com/08.07.06.0017.01









  


  










Input Form





JacobiZeta[z, m] == Exp[(-Pi) I Floor[Arg[z - x]/(2 Pi)]] JacobiZeta[x, m] - JacobiZeta[ArcCsc[Sqrt[m]], m] (1 - Exp[(-Pi) I Floor[Arg[z - x]/(2 Pi)]]) + Exp[(-Pi) I Floor[Arg[z - x]/(2 Pi)]] Sum[(1/k!) Sum[(1/j!) Sum[Binomial[j, q] Sum[((-1)^q 2^(q - j) Sin[x]^q (2 p + q - j)^k Binomial[j - q, p] Sum[((Pochhammer[1 - j, 2 (j - i) - 2]/((j - i - 1)! (2 Sin[x])^ (j - 2 i - 1))) Sum[Binomial[i, s] Pochhammer[1/2, s] Pochhammer[-(1/2), i - s] m^(i - s) Cos[x]^(-1 - 2 s) (1 - m Sin[x]^2)^(1/2 - i + s), {s, 0, i}]) (z - x)^k, {i, 0, j - 1}])/E^((1/2) I ((k - 2 p - q + j) Pi + 2 (2 p + q - j) x)), {p, 0, j - q}], {q, 0, j - 1}], {j, 1, k}], {k, 1, Infinity}] /; Element[x, Reals] && Element[m, Reals] && m > 1 && Pi/2 + Pi u < x < Pi (u + 1) - ArcCsc[Sqrt[m]] && Element[u, Integers]










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