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

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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