EllipticF problem with Maple

Question

When I solve for

EllipticF[1.4, 0.9]

with Mathematica or

ellipticF(1.4, 0.9)

with Mupad I get

2.059

on both. But when I try

EllipticF(1.4, 0.9)

with Maple, I get some complex number

1.036603009 - 1.654616668*I

The result I need is that which I get with Mathematica and Mupad; how do I get it with Maple?

Answer 1

There is a common problem among software libraries that implement special functions: you have to check the definition is the same, and adapt your code accordingly when they are not.

See the definitions for ellipticf in Maple and Mathematica. The arguments are different. In Maple, the first argument is the sine of the amplitude.

For the record, Maxima uses apparently the same definition as Mathematica (I get $2.059$).

See also here on Wikipedia why and how the definitions are different.

Answer 2

Maple and Mathematica use different conventions for the parameters of the elliptic integrals. Maple follows the convention of Gradshteyn and Ryzhik, Mathematica folows Abramowitz and Stegun. Thus Maple's $\text{EllipticF}(x,k)$ is Mathematica's $F(\sin^{-1}(x) \mid k^2)$.