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   

  Eigenvectors and eigenvalues
 Exponential integrals