Legendre Elliptic Integral 1st Kind (Not in Base Package)

Determines the Legendre Elliptic Integral of the 1st kind for the real numbers phi and k (0 is less than or equal to k, which is less than or equal to 1). Details

phi is any real number.
k is a real number with 0 is less than or equal to k, which is less than or equal to 1.
F(phi,k) is the result of the calculation of the Legendre Elliptic integral of the first kind for the given values of phi and k.
error returns any error or warning condition from the VI.

Legendre Elliptic Integral 1st Kind Details

The Legendre Elliptic Integral 1st kind is defined by F(phi,k) = integral of 1/sqrt(1 - k^2*sin(psi)^2) between 0 and phi (psi runs from 0 to phi).

The calculation uses the relation

where is the elliptic integral in the Carlson form