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view scripts/help/bessel.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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## Copyright (C) 1996-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 ## <https://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {[@var{J}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt}) ## @deftypefnx {} {[@var{Y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt}) ## @deftypefnx {} {[@var{I}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt}) ## @deftypefnx {} {[@var{K}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt}) ## @deftypefnx {} {[@var{H}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt}) ## Compute Bessel or Hankel functions of various kinds. ## ## All functions begin with the prefix @qcode{"bessel"}. The list of ## functions is: ## ## @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 @w{@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 @w{@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 @w{@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 ## @w{@code{exp (-I*@var{x})}} for @var{k} = 1 or @w{@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 order of the Bessel function @var{alpha} must be real. The points for ## evaluation @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 ## Loss of significance by argument reduction, output may be inaccurate. ## ## @item ## Error---no computation, algorithm termination condition not met, return ## @code{NaN}. ## @end enumerate ## ## @seealso{besselj, bessely, besseli, besselk, besselh} ## @end deftypefn function bessel () error ("bessel: you must use besselj, bessely, besseli, besselk, or besselh\n"); endfunction %!error bessel ()