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Reference Guide for OpenMatrix Language Functions
The Reference Guide contains documentation for all functions supported in the OpenMatrix language.
Special Functions Commands
besselh
Bessel functions of the first or second kind.

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- Scripting Guide for OpenMatrix Language
  OpenMatrix is a mathematical scripting language.
- Reference Guide for OpenMatrix Language Functions
  The Reference Guide contains documentation for all functions supported in the OpenMatrix language.
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    - besselh
      Bessel functions of the first or second kind.
    - besseli
      Modified Bessel function of the first kind.
    - besselj
      Bessel function of the first kind.
    - besselk
      Modified Bessel function of the second kind.
    - bessely
      Bessel function of the second kind.
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besselh

Bessel functions of the first or second kind.

Syntax

[h,ierr] = besselh(alpha, k, x, opt)

Inputs

alpha: The function order.; Type: double; Dimension: scalar | vector | matrix
k: The function kind, either 1 or 2.; Dimension: scalar
x: The function argument.; Type: double | complex; Dimension: scalar | vector | matrix
opt: The scaling option.; If set to 1 or true the result contains a factor of exp(-ix) when k = 1 or exp(ix) when k = 2.; Dimension: scalar | vector | matrix

Outputs

h

The Bessel function values.

Dimension: scalar | vector | matrix

ierr

The return status flag.

Dimension: scalar | vector | matrix

info = 0: Successful return.
info = 1: Input error, returned NaN.
info = 2: Overflow condition, returned Inf.
info = 3: Calculation has lost at least half of machine accuracy.
info = 4: Calculation has lost significance, returned NaN.
info = 5: Algorithm failed to converge, returned NaN.

Examples

Unscaled example:

h = besselh(3,1,[10:12;13:15])

h = [Matrix] 2 x 3
0.05838 - 0.25136i   0.22735 - 0.09148i   0.19514 + 0.12901i
0.00332 + 0.22420i  -0.17681 + 0.12350i  -0.19402 - 0.07511i

Scaled example:

h = besselh(3,2,[10:12;13:15],1)

h = [Matrix] 2 x 3
0.08776 - 0.24267i  0.09249 - 0.22694i  0.09545 - 0.21357i
0.09721 - 0.20206i  0.09817 - 0.19204i  0.09855 - 0.18323i

Comments

If alpha and x have different dimensions, a singleton dimension in either variable is expanded to match the corresponding dimension length of the other variable.