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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
bessely
Bessel function of the 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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bessely

Bessel function of the second kind.

Syntax

[y,ierr] = bessely(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(real(x))).; Dimension: scalar | vector | matrix

Outputs

y

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:

y = bessely(3,[10:12;13:15]*i)

y = [Matrix] 2 x 3
1.75838e+03 - 1.73496e-05i  4.75793e+03 - 5.87102e-06i  1.28329e+04 - 2.00639e-06i
3.45380e+04 - 6.91133e-07i  9.28206e+04 - 2.39628e-07i  2.49218e+05 - 8.35453e-08i

Scaled example:

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

y = [Matrix] 2 x 3
7.98304e-02 - 7.87671e-10i  7.94655e-02 - 9.80561e-11i  7.88480e-02 - 1.23277e-11i
7.80672e-02 - 1.56219e-12i  7.71830e-02 - 1.99257e-13i  7.62365e-02 - 2.55567e-14i

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.