Inverse of the Jacobi elliptic function cn: Differentiation (formula 09.38.20.0012)

InverseJacobiCN

$Mathematica Notation$

Elliptic Functions

InverseJacobiCN[z,m]

Differentiation

Low-order differentiation

With respect to m

http://functions.wolfram.com/09.38.20.0012.01

Input Form

D[InverseJacobiCN[z, m], {m, 3}] == (-(1/(8 (-1 + m)^3 m^3))) ((-1 + m) (8 + m (-19 + 15 m)) InverseJacobiCN[z, m] + (1/(1 + m (-1 + z^2))^3) ((8 + 23 (-1 + m) m) (1 + m (-1 + z^2))^3 EllipticE[JacobiAmplitude[InverseJacobiCN[z, m], m], m] + m z (-1 + z^2) ((-1 + m)^2 (4 + m (-12 + 23 m)) - (-1 + m) m (9 + m (-35 + 46 m)) z^2 + m^2 (8 + 23 (-1 + m) m) z^4) JacobiDS[InverseJacobiCN[z, m], m]))

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