Elliptic integrals

Syntax: | `y = FINELLIC(x,p) y = ELLICK(x) y = EINELLIC(x,p) y = ELLICE(x)`

Elliptic integrals have the form

where is a rational function of x and y, and y2 is a cubic or quartic polynomial in x. Any elliptic integral can be expressed in terms of the three canonical forms. The elliptic integrals are said to be "complete" when the amplitude is .

First kind

For and

For

Second kind

For and

For