Inverse of the Jacobi elliptic function dn: Differentiation (formula 09.41.20.0007)

InverseJacobiDN

$Mathematica Notation$

Elliptic Functions

InverseJacobiDN[z,m]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/09.41.20.0007.01

Input Form

D[InverseJacobiDN[z, m], {z, n}] == (-((2^(-1 + n) Pi z^(-1 + n) (-1 + n)! JacobiCS[InverseJacobiDN[z, m], m])/ (-1 + m + z^2))) Sum[((m + z^2 - 1)^(1 + j - n)/ ((z^2 - 1)^j (j! (n - j - 1)! Gamma[1/2 - j] Gamma[3/2 + j - n]))) Hypergeometric2F1[(1 - j)/2, -(j/2), 1/2 - j, 1 - 1/z^2] Hypergeometric2F1[(2 + j - n)/2, (1 + j - n)/2, 3/2 + j - n, 1 + (m - 1)/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)

2001-10-29