# Spherical Bessel Function jn (G Dataflow)

Calculates the spherical Bessel function of the first kind.

## x

Input argument.

This input accepts a double-precision, floating-point number or a complex double-precision, floating-point number.

Default: The default value is 0 if x is a double-precision, floating-point number. The default value is 0 + 0i if x is a complex double-precision, floating-point number.

## n

Order of the spherical Bessel function.

## 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

## jn(x)

Value of the spherical Bessel function of the first kind.

This output can return a double-precision, floating-point number or a complex double-precision, floating-point number.

## 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 Calculating the Spherical Bessel Function of the First Kind

For the spherical Bessel function of the first kind of order n, jn(x) is a solution to the following differential equation.

${x}^{2}\frac{{d}^{2}w}{d{x}^{2}}+2x\frac{dw}{dx}+\left({x}^{2}-n\left(n+1\right)\right)w=0$

The following equation shows the relationship of the spherical Bessel function of the first kind to the Bessel function of the first kind.

${j}_{n}\left(x\right)=\sqrt{\frac{\pi }{2x}}{J}_{v}\left(x\right),v=n+\frac{1}{2}$

The function is defined according to the following intervals for the input values.

$n\in \Im ,x\in \left[0,\infty \right)$

This node supports the entire domain of this function that produces real-valued results. For any integer value of order n, the function is defined for nonnegative real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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