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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
besselj
Bessel function of the first 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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besselj

Bessel function of the first kind.

Syntax

[j,ierr] = besselj(alpha, x, opt)

Inputs

alpha: The function order.; Type: double; Dimension: scalar | vector | matrix
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(-abs(imag(x))).; Dimension: scalar | vector | matrix

Outputs

j

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:

j = besselj(3,[10:12;13:15]*i)

j = [Matrix] 2 x 3
-1.07670e-13 - 1.75838e+03i  -2.91339e-13 - 4.75793e+03i  -7.85788e-13 - 1.28329e+04i
-2.11484e-12 - 3.45380e+04i  -5.68362e-12 - 9.28206e+04i  -1.52602e-11 - 2.49218e+05i

Scaled example:

j = besselj(3,[10:12;13:15]*i,1)

j = [Matrix] 2 x 3
-4.88820e-18 - 7.98304e-02i  -4.86586e-18 - 7.94655e-02i  -4.82805e-18 - 7.88480e-02i
-4.78024e-18 - 7.80672e-02i  -4.72610e-18 - 7.71830e-02i  -4.66814e-18 - 7.62365e-02i

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.