..
  Copyright 1988-2021 Free Software Foundation, Inc.
  This is part of the GCC manual.
  For copying conditions, see the GPL license file

.. _bessel_yn:

BESSEL_YN --- Bessel function of the second kind
************************************************

.. index:: BESSEL_YN

.. index:: BESYN

.. index:: DBESYN

.. index:: Bessel function, second kind

.. function:: BESSEL_YN(N, X)

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

  :param N:
    Shall be a scalar or an array of type  ``INTEGER`` .

  :param N1:
    Shall be a non-negative scalar of type  ``INTEGER``.

  :param N2:
    Shall be a non-negative scalar of type  ``INTEGER``.

  :param X:
    Shall be a scalar or an array of type  ``REAL`` ;
    for ``BESSEL_YN(N1, N2, X)`` it shall be scalar.

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

  :samp:`{Standard}:`
    Fortran 2008 and later, negative :samp:`{N}` is allowed as GNU extension

  :samp:`{Class}:`
    Elemental function, except for the transformational function
    ``BESSEL_YN(N1, N2, X)``

  :samp:`{Syntax}:`

  .. code-block:: fortran

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

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

  :samp:`{Example}:`

    .. code-block:: fortran

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

  :samp:`{Specific names}:`
    ===============  =============  ===========  =============
    Name             Argument       Return type  Standard
    ===============  =============  ===========  =============
    ``DBESYN(N,X)``  ``INTEGER N``  ``REAL(8)``  GNU extension
                     ``REAL(8) X``
    ===============  =============  ===========  =============