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Owning Class: advanced
Requires: MathScript RT Module
sh = sphbessel_h(v, x)
sh = sphbessel_h(v, kind, x)
sh = sphbessel_h(v, kind, x, 1)
[sh, error] = sphbessel_h(v, x)
[sh, error] = sphbessel_h(v, kind, x)
[sh, error] = sphbessel_h(v, kind, x, 1)
Legacy Name: sphbesselh
Computes the spherical Bessel function of the third kind of a given order. sphbessel_h(v, x) is equivalent to sphbessel_h(v, 1, x) and corresponds to the Hankel function of the first kind. sphbessel_h(v, 2, x) corresponds to the Hankel function of the second kind.
Name  Description  

v  Specifies the order of the spherical Bessel function. v is a real, doubleprecision, floatingpoint positive scalar, vector, or matrix and must be integervalued.  
x  Specifies the value for which you want to compute the spherical Bessel function. x is a real or complex, doubleprecision, floatingpoint scalar, vector, or matrix.  
kind  Specifies the type of the Hankel function. kind is an integer that accepts the following values.


1  Scales the computation. sphbessel_h(v, 1, x, 1) scales sphbessel_h(v, 1, x) by exp(i*x). sphbessel_h(v, 2, x, 1) scales sphbessel_h(v, 2, x) by exp(i*x). 
Name  Description  

sh  Returns the spherical Bessel function of the third kind. sh is a real or complex, doubleprecision, floatingpoint scalar, vector, or matrix.  
error  Returns error information about the evaluation of the spherical Bessel function. error is a matrix of integers in which each element can return the following values.

The spherical Bessel functions are defined as particular solutions to the following equation. This equation comes from solving the Helmholtz in spherical coordinates. When you solve the Helmholtz equation in spherical coordinates using the separation of variables, the radial differential equation becomes the following equation:
x^{2}y'' + 2xy' + [x^{2}  n(n + 1)]y = 0 (n = 0, ±1, ±2, ...)
Particular solutions to this equation are known as the spherical Bessel functions of the first kind, j(v, x), and second kind, y(v, x). You can write the particular solutions to this equation as functions of the following ordinary Bessel functions:
j(v, x) = sqrt(x*pi / 2)*J(v + 1/2, x)
y(v, x) = sqrt(x*pi / 2)*Y(v + 1/2, x)
The following equations define the spherical Bessel functions of the third kind, which are also known as spherical Hankel functions:
h1(v, x) = j(v, x) + i*y(v, x)
h2(v, x) = j(v, x)  i*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 specify in x. If v is a scalar, LabVIEW sets v to a vector of the same size as x whose elements all equal the value you specify in v. If x and v are vectors of the same orientation, LabVIEW returns a vector of spherical Bessel functions for the corresponding input values. For example, if x equals [1, 2] and v equals [3, 4], LabVIEW returns [sphbessel_h(1, 3), sphbessel_h(2, 4)]. If x and v are vectors of opposite orientation, LabVIEW returns a matrix of spherical Bessel functions for each combination of input values. For example, if x equals [1, 2] and v = [3; 4], LabVIEW returns [sphbessel_h(1, 3), sphbessel_h(1, 4); sphbessel_h(2, 3), sphbessel_h(2, 4)].
The following table lists the support characteristics of this function.
Supported in the LabVIEW RunTime Engine  Yes 
Supported on RT targets  Yes 
Suitable for bounded execution times on RT  Not characterized 
X = [0:0.01:5];
sh0 = sphbessel_h(0, 1, X);
sh1 = sphbessel_h(1, 1, X);
sh2 = sphbessel_h(2, 1, X);
plot(X, real(sh0), X, real(sh1), X, real(sh2));
axis([0, 5, 2, 2]);
bessel_h
bessel_i
bessel_j
bessel_k
bessel_y
sphbessel_j
sphbessel_y
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