Function of the Day: Complete Elliptic Integral

Today's function of the day is the complete elliptic integral. These functions are included in the package "functions". The complete elliptic integral of the first kind is defined as

\(K(m) = \int_0^{\pi/2} [1-m\sin(t)^2]^{-1/2} dt\)

and can be used from Gaea as following:

(require :functions)
(functions:ellipk 1)

The complete elliptic integral of the second kind is defined as

\(E(m) = \int_0^{\pi/2} [1-m\sin(t)^2]^{1/2} dt\)

which can used from Gaea as following:

(require :functions) 
(functions:ellipe 1)

Have fun!