Inverse of the Jacobi elliptic function sd: Differentiation (formula 09.47.20.0014)

InverseJacobiSD

$Mathematica Notation$

Elliptic Functions

InverseJacobiSD[z,m]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/09.47.20.0014.01

Input Form

D[InverseJacobiSD[z, m], {z, n}] == KroneckerDelta[n] InverseJacobiSD[z, m] + (JacobiCN[InverseJacobiSD[z, m], m]/(1 + (-1 + m) z^2)) Sum[((1/(-1 - j + n)!) (((-1)^j 2^(1 + 2 j - n) m^j z^(1 + 2 j - n) Pochhammer[1/2, j] Pochhammer[1 - n, -2 + 2 (-j + n)])/ (1 - (1 - m) z^2)^j)) ((-1 + m)/m)^j Hypergeometric2F1[1/2, -j, 1/2 - j, (m (1 - z^2 + m z^2))/((-1 + m) (1 + m z^2))], {j, 0, n - 1}] /; Element[n, Integers] && n >= 0

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