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Operators and Keywords

Function List:

C++ API

: [j, ierr] = besselj (alpha, x, opt)
: [y, ierr] = bessely (alpha, x, opt)
: [i, ierr] = besseli (alpha, x, opt)
: [k, ierr] = besselk (alpha, x, opt)
: [h, ierr] = besselh (alpha, k, x, opt)

Compute Bessel or Hankel functions of various kinds:

besselj

Bessel functions of the first kind. If the argument opt is 1 or true, the result is multiplied by exp (-abs (imag (x))).

bessely

Bessel functions of the second kind. If the argument opt is 1 or true, the result is multiplied by exp (-abs (imag (x))).

besseli

Modified Bessel functions of the first kind. If the argument opt is 1 or true, the result is multiplied by exp (-abs (real (x))).

besselk

Modified Bessel functions of the second kind. If the argument opt is 1 or true, the result is multiplied by exp (x).

besselh

Compute Hankel functions of the first (k = 1) or second (k = 2) kind. If the argument opt is 1 or true, the result is multiplied by exp (-I*x) for k = 1 or exp (I*x) for k = 2.

If alpha is a scalar, the result is the same size as x. If x is a scalar, the result is the same size as alpha. If alpha is a row vector and x is a column vector, the result is a matrix with length (x) rows and length (alpha) columns. Otherwise, alpha and x must conform and the result will be the same size.

The value of alpha must be real. The value of x may be complex.

If requested, ierr contains the following status information and is the same size as the result.

  1. Normal return.
  2. Input error, return NaN.
  3. Overflow, return Inf.
  4. Loss of significance by argument reduction results in less than half of machine accuracy.
  5. Complete loss of significance by argument reduction, return NaN.
  6. Error—no computation, algorithm termination condition not met, return NaN.

Package: octave