# bessel_h (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Requires: MathScript RT Module

## Syntax

hv = bessel_h(v, x)

hv = bessel_h(v, kind, x)

hv = bessel_h(v, kind, x, 1)

[hv, error] = bessel_h(v, x)

[hv, error] = bessel_h(v, kind, x)

[hv, error] = bessel_h(v, kind, x, 1)

Legacy Name: `besselh`

## Description

Computes the Bessel function of the third kind, or the Hankel function, of a given order. bessel_h(v, x) is equivalent to bessel_h(v, 1, x).

Details

Examples

## Inputs

Name Description
v Specifies the order of the Hankel function. v is a real, double-precision, floating-point, positive scalar, vector, or matrix.
x Specifies the value for which you want to compute the Hankel function. x is a real or complex, double-precision, floating-point scalar, vector, or matrix.
kind Specifies the type of the Hankel function. kind is an integer that accepts the following values.

 1 Computes the Hankel function of the first kind. 2 Computes the Hankel function of the second kind.
1 Scales the computation. bessel_h(v, 1, x, 1) scales bessel_h(v, 1, x) by exp(-i*x). bessel_h(v, 2, x, 1) scales bessel_h(v, 2, x) by exp(i*x).

## Outputs

Name Description
hv Returns the Hankel function. hv is a real or complex, double-precision, floating-point scalar, vector, or matrix.
error Returns error information about the evaluation of the Hankel function. error is a matrix of integers in which each element can return the following values.

 0 Indicates that no error occurred. 1 Indicates that you specified invalid inputs. 2 Indicates that the result is too large for the data type of hv. Use the scaling option 1. 3 Indicates that LabVIEW achieved less than half the machine accuracy in the calculation because |x| or v is greater than approximately 1.3E8. 4 Indicates that the result is meaningless because |x| or v is greater than approximately 1.8E16. 5 Indicates that the calculation did not reach the termination condition so LabVIEW did not complete the calculation.

## Details

LabVIEW computes the Hankel functions, which are defined by:
bessel_h(v, 1, x) = bessel_j(v, x)+i*bessel_y(v, x)
bessel_h(v, 2, x) = bessel_j(v, x)-i*bessel_y(v, x)

If x is a scalar, LabVIEW sets x to a vector of the same size as v whose elements all equal the value you specified for x. If y is a scalar, LabVIEW sets y to a vector of the same size as v whose elements all equal the value you specified for y. If x and v are vectors of the same orientation, LabVIEW returns a vector of Hankel functions for corresponding input values. For example, if x = [1, 2] and v = [3, 4], LabVIEW returns [bessel_h(1, 3), bessel_h(2, 4)]. If x and v are vectors of opposite orientation, LabVIEW returns a matrix of Hankel functions for each combination of input values. For example, if x = [1, 2] and v = [3; 4], LabVIEW returns [bessel_h(1, 3), bessel_h(1, 4); bessel_h(2, 3), bessel_h(2, 4)].

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

## Examples

X = [0.1:0.099:2];
HV = bessel_h(2, 1, X);
plot(X, HV)