Elliptic integral
In integral calculus, an elliptic integral is any function f which can be expressed in the form
where R is a rational function of its two arguments, P is the square root of a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.
Particular examples include:
- The complete elliptic integral of the first kind K is defined as
- The complete elliptic integral of the second kind E is defined as
Historically properties of these integrals were studied in connection with the problem of the arc length of an ellipse, by Fagnano and Leonhard Euler.The origin of the name
