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Question: Maple description of elliptic integrals

Question:Maple description of elliptic integrals

C_R 3042 Maple
special-function elliptic-integral documentation ellipticf
September 24 2023
2

In help(EllipticF): Why is the parameter k not called “the modulus of the elliptic function” as in the definition of the inverse Jacobi functions in help(InverseJacobiPQ)?

Instead, it is called “the parameter” which can be confused with the parameter m=k^2 used in other notations (which is refered to "a parameter m" in the EllipticF help page).

Is there a reason for this, or should the parameter definitions of the first, second and thrid elliptic integrals not be aligned with the parameter definitions of the Jacobi functions and their inverses?

DLMF for example defines k as modulus for both, the Elliptic Integrals and the Jacobian Elliptic Functions.

A user who wants to transfer an expression from a different notation to Maple might misinterpret parameters.

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