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

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.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

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.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## 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: This product does not support FPGA devices

Web Server: Not supported in VIs that run in a web application