Special case of elliptic integral (M = arithmetic geometric mean)

lanxiyu · 2023-11-10 22:00:26

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Duplication formulas:

Definition of Jacobi zeta function:

Derivatives:

k-derivatives:

Lemniscatic cases:

Degenerate cases:

Reciprocal modulus transformation (if 0<k<1):

Perimeter of ellipse with semiaxes x, y:

Surface area of ellipsoid with semiaxes x, y, z:

Definition of Legendre’s elliptic Integrals
Notation for the theta functions

Last edited by lanxiyu (2025-04-14 03:41:13)

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#1 2023-11-10 22:00:26

Special case of elliptic integral (M = arithmetic geometric mean)

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