BESSEL_YN (The GNU Fortran Compiler)

### 8.49 `BESSEL_YN` — Bessel function of the second kind ¶

Synopsis:

  `RESULT = BESSEL_YN(N, X)`
  `RESULT = BESSEL_YN(N1, N2, X)`

Description:

  `BESSEL_YN(N, X)` computes the Bessel function of the second kind of order N of X. This function is available under the name `BESYN` as a GNU extension. If N and X are arrays, their ranks and shapes shall conform.

  `BESSEL_YN(N1, N2, X)` returns an array with the Bessel functions of the first kind of the orders N1 to N2.

Class:

  Elemental function, except for the transformational function `BESSEL_YN(N1, N2, X)`

Arguments:

  N | Shall be a scalar or an array of type `INTEGER` .
  N1 | Shall be a non-negative scalar of type `INTEGER`.
  N2 | Shall be a non-negative scalar of type `INTEGER`.
  X | Shall be a scalar or an array of type `REAL`; for `BESSEL_YN(N1, N2, X)` it shall be scalar.

Return value:

  The return value is a scalar of type `REAL`. It has the same kind as X.

Notes:

  The transformational function uses a recurrence algorithm which might, for some values of X, lead to different results than calls to the elemental function.

Example:

      program test_besyn
        real(8) :: x = 1.0_8
        x = bessel_yn(5,x)
      end program test_besyn

Specific names:

  Name | Argument | Return type | Standard
  --- | --- | --- | ---
  `DBESYN(N,X)` | `INTEGER N` | `REAL(8)` | GNU extension
  | `REAL(8) X` |  |

Standard:

  Fortran 2008 and later, negative N is allowed as GNU extension