Definition:Elliptic Integral

Special Function
An elliptic integral is an integral in the form:
 * $\displaystyle \int_0^x R \left({t, \sqrt {P \left({t}\right)} }\right) \, \mathrm d t$

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

There exist some special cases: