Derivative of the Weierstrass elliptic function: Differentiation (formula 09.14.20.0006)

WeierstrassPPrime

$Mathematica Notation$

Elliptic Functions

WeierstrassPPrime[z,{g₂,g₃}]

Differentiation

Low-order differentiation

With respect to g₃

http://functions.wolfram.com/09.14.20.0006.01

Input Form

D[WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}], Subscript[g, 3]] == (1/(4 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2))) (9 z Subscript[g, 2] Subscript[g, 3] - 108 z Subscript[g, 3] WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + (-54 Subscript[g, 3] + 36 Subscript[g, 2] WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]) WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + (-6 Subscript[g, 2]^2 + 72 Subscript[g, 2] WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2) WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])

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