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maint: Update copyright dates in all source files.
author John W. Eaton <jwe@octave.org>
date Wed, 02 Jan 2019 16:32:43 -0500
parents d7ad543255c5
children b442ec6dda5c
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1 ## Copyright (C) 1996-2019 John W. Eaton
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software: you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation, either version 3 of the License, or
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8 ## (at your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 ## GNU General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {[@var{J}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt})
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21 ## @deftypefnx {} {[@var{Y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})
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22 ## @deftypefnx {} {[@var{I}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})
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23 ## @deftypefnx {} {[@var{K}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})
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24 ## @deftypefnx {} {[@var{H}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt})
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25 ## Compute Bessel or Hankel functions of various kinds.
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26 ##
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27 ## All functions begin with the prefix @qcode{"bessel"}. The list of
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28 ## functions is:
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29 ##
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30 ## @table @code
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31 ## @item besselj
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32 ## Bessel functions of the first kind. If the argument @var{opt} is supplied,
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33 ## the result is multiplied by @code{exp (-abs (imag (x)))}.
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34 ##
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35 ## @item bessely
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36 ## Bessel functions of the second kind. If the argument @var{opt} is supplied,
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37 ## the result is multiplied by @w{@code{exp (-abs (imag (x)))}}.
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38 ##
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39 ## @item besseli
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40 ## Modified Bessel functions of the first kind. If the argument @var{opt} is
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41 ## supplied, the result is multiplied by @w{@code{exp (-abs (real (x)))}}.
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42 ##
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43 ## @item besselk
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44 ## Modified Bessel functions of the second kind. If the argument @var{opt} is
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45 ## supplied, the result is multiplied by @w{@code{exp (x)}}.
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46 ##
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47 ## @item besselh
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48 ## Compute Hankel functions of the first (@var{k} = 1) or second (@var{k} = 2)
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49 ## kind. If the argument @var{opt} is supplied, the result is multiplied by
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50 ## @w{@code{exp (-I*@var{x})}} for @var{k} = 1 or @w{@code{exp (I*@var{x})}}
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51 ## for @var{k} = 2.
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52 ## @end table
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53 ##
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54 ## If @var{alpha} is a scalar, the result is the same size as @var{x}. If
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55 ## @var{x} is a scalar, the result is the same size as @var{alpha}. If
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56 ## @var{alpha} is a row vector and @var{x} is a column vector, the result is
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57 ## a matrix with @code{length (@var{x})} rows and @code{length
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58 ## (@var{alpha})} columns. Otherwise, @var{alpha} and @var{x} must conform
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59 ## and the result will be the same size.
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60 ##
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61 ## The order of the Bessel function @var{alpha} must be real. The points for
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62 ## evaluation @var{x} may be complex.
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63 ##
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64 ## If requested, @var{ierr} contains the following status information and is
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65 ## the same size as the result.
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66 ##
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67 ## @enumerate 0
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68 ## @item
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69 ## Normal return.
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70 ##
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71 ## @item
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72 ## Input error, return @code{NaN}.
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73 ##
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74 ## @item
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75 ## Overflow, return @code{Inf}.
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76 ##
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77 ## @item
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78 ## Loss of significance by argument reduction results in less than half of
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79 ## machine accuracy.
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80 ##
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81 ## @item
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82 ## Loss of significance by argument reduction, output may be inaccurate.
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83 ##
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84 ## @item
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85 ## Error---no computation, algorithm termination condition not met, return
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86 ## @code{NaN}.
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87 ## @end enumerate
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88 ##
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89 ## @seealso{besselj, bessely, besseli, besselk, besselh}
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90 ## @end deftypefn
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92 function bessel ()
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93 error ("bessel: you must use besselj, bessely, besseli, besselk, or besselh\n");
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94 endfunction
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95
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97 %!error bessel ()