# Elliptic Integral of the 1st Kind (Incomplete Elliptic Integral F) (G Dataflow)

Version:
Last Modified: January 9, 2017

Computes the incomplete Legendre elliptic integral of the first kind.

## k

The modulus argument. k is a real number between 0 and 1.

## a

The amplitude of the function, which is the upper limit of the integral.

Default: Pi/2

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## F(k, a)

Value of the incomplete elliptic integral of the first kind.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Computing the Incomplete Elliptic Integral of the First Kind

The following equation defines the incomplete elliptic integral of the first kind.

$F\left(k,a\right)={\int }_{0}^{a}\frac{1}{\sqrt{1-k{\mathrm{sin}}^{2}\theta }}d\theta$

The following intervals for the input values define the function.

$a\in \Re ,k\in \left[0,1\right]$

This node supports the entire domain of this function that produces real-valued results. For a real value of upper limit a, the function is defined for all real values of k in the unit interval.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported