# Incomplete elliptic integral of first kind F(`phi`,k)

`F(phi,k) = \int_0^phi \ 1/sqrt(1-k^2*sin^2 theta) d theta` `-1<=k<=1`

This tool is a calculator of incomplete elliptic integral of first kind.

`F(phi,k) = \int_0^phi \ 1/sqrt(1-k^2*sin^2 theta) d theta`

`phi` : amplitude

k : module or eccentricity ( -1 <= k <= 1)

By substituting `x = sin(phi)` and `t = sin(theta)`, we obtain another form of the same function :

Incomplete elliptic integral of first kind (x)

## See also

### Incomplete Integral Calculators

incomplete elliptic integral of second kind (`phi`)incomplete elliptic integral of second kind (`x`)

incomplete elliptic integral of third kind (`phi`)

incomplete elliptic integral of third kind (`x`)

### Complete Integral Calculators

Complete elliptic integral of first kindComplete elliptic integral of second kind

Complete elliptic integral of third kind

### Other Calculators

Special functions Calculators

Mathématics Calculators