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JacobiNC






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.31.06.0006.01









  


  










Input Form





JacobiNC[z, m] == Sum[(k + 1) Sum[(((-1)^r Binomial[k, r])/(1 + r)) Subscript[p, r, k] z^(2 k), {r, 0, k}], {k, 0, Infinity}] /; Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j i - k + i) (((-1)^i Subscript[cn, i][m])/(2 i)!) Subscript[p, j, k - i], {i, 1, k}] && Element[k, Integers] && k > 0 && Subscript[sn, 0][m] == 1 && Subscript[sn, n][m] == Sum[Binomial[2 n, 2 j] Subscript[cn, j][m] Subscript[dn, k][m] KroneckerDelta[j + k - n], {j, 0, n}, {k, 0, n}] && Subscript[cn, 0][m] == 1 && Subscript[cn, n][m] == Sum[Binomial[2 n - 1, 2 j + 1] Subscript[sn, j][m] Subscript[dn, k][m] KroneckerDelta[j + k - n + 1], {j, 0, n - 1}, {k, 0, n - 1}] && Subscript[dn, 0][m] == 1 && Subscript[dn, n][m] == m Sum[Binomial[2 n - 1, 2 j + 1] Subscript[sn, j][m] Subscript[cn, k][m] KroneckerDelta[j + k - n + 1], {j, 0, n - 1}, {k, 0, n - 1}]










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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