update packages

[CreaPhase.git] / octave_packages / m / specfun / bessel.m

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+## Copyright (C) 1996-2012 John W. Eaton
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Loadable Function} {[@var{j}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt})
+## @deftypefnx {Loadable Function} {[@var{y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})
+## @deftypefnx {Loadable Function} {[@var{i}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})
+## @deftypefnx {Loadable Function} {[@var{k}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})
+## @deftypefnx {Loadable Function} {[@var{h}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt})
+## Compute Bessel or Hankel functions of various kinds:
+##
+## @table @code
+## @item besselj
+## Bessel functions of the first kind.  If the argument @var{opt} is supplied,
+## the result is multiplied by @code{exp(-abs(imag(x)))}.
+##
+## @item bessely
+## Bessel functions of the second kind.  If the argument @var{opt} is supplied,
+## the result is multiplied by @code{exp(-abs(imag(x)))}.
+##
+## @item besseli
+## Modified Bessel functions of the first kind.  If the argument @var{opt} is
+## supplied,
+## the result is multiplied by @code{exp(-abs(real(x)))}.
+##
+## @item besselk
+## Modified Bessel functions of the second kind.  If the argument @var{opt} is
+## supplied,
+## the result is multiplied by @code{exp(x)}.
+##
+## @item besselh
+## Compute Hankel functions of the first (@var{k} = 1) or second (@var{k}
+## = 2) kind.  If the argument @var{opt} is supplied, the result is multiplied
+## by
+## @code{exp (-I*@var{x})} for @var{k} = 1 or @code{exp (I*@var{x})} for
+## @var{k} = 2.
+## @end table
+##
+## If @var{alpha} is a scalar, the result is the same size as @var{x}.
+## If @var{x} is a scalar, the result is the same size as @var{alpha}.
+## If @var{alpha} is a row vector and @var{x} is a column vector, the
+## result is a matrix with @code{length (@var{x})} rows and
+## @code{length (@var{alpha})} columns.  Otherwise, @var{alpha} and
+## @var{x} must conform and the result will be the same size.
+##
+## The value of @var{alpha} must be real.  The value of @var{x} may be
+## complex.
+##
+## If requested, @var{ierr} contains the following status information
+## and is the same size as the result.
+##
+## @enumerate 0
+## @item
+## Normal return.
+##
+## @item
+## Input error, return @code{NaN}.
+##
+## @item
+## Overflow, return @code{Inf}.
+##
+## @item
+## Loss of significance by argument reduction results in less than
+## half of machine accuracy.
+##
+## @item
+## Complete loss of significance by argument reduction, return @code{NaN}.
+##
+## @item
+## Error---no computation, algorithm termination condition not met,
+## return @code{NaN}.
+## @end enumerate
+## @end deftypefn
+
+function bessel ()
+  error ("bessel: you must use besselj, bessely, besseli, or besselk");
+endfunction
+
+%!error bessel ()