## Elliptic Integral of the 1st Kind

This tool evaluates the complete or incomplete elliptic integral of the first kind: K(k) or F(φ,k) respectively. Select the desired type of the calculation and enter the appropriate arguments below.

 Type Complete Incomplete k = Result:

## About Elliptic Integrals of the First Kind

### Definitions

The incomplete elliptic integral of the first kind is defined as:

where k is the elliptic modulus, with . Variable is the Jacobi's amplitude.

The complete elliptic integral of the first kind is defined as: