..
  Copyright 1988-2022 Free Software Foundation, Inc.
  This is part of the GCC manual.
  For copying conditions, see the copyright.rst file.

.. _bessel_jn:

.. index:: BESSEL_JN

.. index:: BESJN

.. index:: DBESJN

.. index:: Bessel function, first kind

BESSEL_JN --- Bessel function of the first kind
***********************************************

.. function:: BESSEL_JN(N, X)

  ``BESSEL_JN(N, X)`` computes the Bessel function of the first kind of
  order :samp:`{N}` of :samp:`{X}`. This function is available under the name
  ``BESJN`` 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_JN(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}`.

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

  Class:
    Elemental function, except for the transformational function
    ``BESSEL_JN(N1, N2, X)``

  Syntax:
    .. code-block:: fortran

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

  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.

  Example:
    .. code-block:: fortran

      program test_besjn
        real(8) :: x = 1.0_8
        x = bessel_jn(5,x)
      end program test_besjn

  Specific names:
    .. list-table::
       :header-rows: 1

       * - Name
         - Argument
         - Return type
         - Standard

       * - ``DBESJN(N, X)``
         - ``INTEGER N``
         - ``REAL(8)``
         - GNU extension
       * -
         - ``REAL(8) X``
         -
         -