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JacobiNC




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiNC[z,m] > Series representations > Generalized power series > Expansions at z==(2 r+1) K(m)+2 i s K(1-m)





http://functions.wolfram.com/09.31.06.0009.01









  


  








Input Form





JacobiNC[z, m] == ((-1)^(r + s - 1)/Sqrt[1 - m]) Sum[(j + 1) (((-1)^(k - j) Subscript[dn, k - j][m])/(2 k - 2 j)!) Sum[(((-1)^r Binomial[j, r])/(1 + r)) Subscript[q, r, j] (z - Subscript[z, 0])^(2 k - 1), {r, 0, j}], {k, 0, Infinity}, {j, 0, k}] /; Subscript[z, 0] == (2 r + 1) EllipticK[m] + 2 s I EllipticK[1 - m] && Element[r, Integers] && Element[s, Integers] && Subscript[q, j, 0] == 1 && Subscript[q, j, k] == (1/k) Sum[(j i - k + i) (((-1)^i Subscript[sn, i][m])/(2 i + 1)!) Subscript[q, 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