Definition:Elliptic Integral

Special Function
An elliptic integral is an integral in the form:
 * $\ds \int_0^x \map R {t, \sqrt {\map P t} } \rd t$

where:
 * $\map P t$ is a polynomial of degree $3$ or $4$
 * $\map R {t, \sqrt {\map P t} }$ is a rational function of $t$ and $\sqrt {\map P t}$.

There exist some special cases: