An elliptic integral is an integral of a rational function of and , where is a cubic or quartic polynomial with distinct roots. The standard first, second and third kinds describe the essential normal forms. Choosing the full endpoint yields complete versions such as the complete elliptic integral of the first kind.
Articles by others on the same topic
An elliptic integral is a type of integral that arises in the calculation of the arc length of an ellipse, as well as in various problems of physics and engineering. Elliptic integrals are generally not expressible in terms of elementary functions, which means that their solutions cannot be represented using basic algebraic operations and standard functions (like polynomials, exponentials, trigonometric functions, etc.).