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author David Bateman <dbateman@free.fr>
date Sun, 06 Feb 2011 23:59:37 +0100
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1996-2011 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 (at
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8 ## 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 GNU
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13 ## 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 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Loadable Function} {[@var{j}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt})
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21 ## @deftypefnx {Loadable Function} {[@var{y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})
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22 ## @deftypefnx {Loadable Function} {[@var{i}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})
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23 ## @deftypefnx {Loadable Function} {[@var{k}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})
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24 ## @deftypefnx {Loadable Function} {[@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 ## @table @code
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28 ## @item besselj
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29 ## Bessel functions of the first kind. If the argument @var{opt} is supplied,
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30 ## the result is multiplied by @code{exp(-abs(imag(x)))}.
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31 ##
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32 ## @item bessely
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33 ## Bessel functions of the second kind. If the argument @var{opt} is supplied,
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34 ## the result is multiplied by @code{exp(-abs(imag(x)))}.
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35 ##
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36 ## @item besseli
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37 ## Modified Bessel functions of the first kind. If the argument @var{opt} is
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38 ## supplied,
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39 ## the result is multiplied by @code{exp(-abs(real(x)))}.
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40 ##
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41 ## @item besselk
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42 ## Modified Bessel functions of the second kind. If the argument @var{opt} is
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43 ## supplied,
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44 ## the result is multiplied by @code{exp(x)}.
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45 ##
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46 ## @item besselh
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47 ## Compute Hankel functions of the first (@var{k} = 1) or second (@var{k}
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48 ## = 2) kind. If the argument @var{opt} is supplied, the result is multiplied
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49 ## by
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50 ## @code{exp (-I*@var{x})} for @var{k} = 1 or @code{exp (I*@var{x})} for
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51 ## @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}.
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55 ## If @var{x} is a scalar, the result is the same size as @var{alpha}.
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56 ## If @var{alpha} is a row vector and @var{x} is a column vector, the
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57 ## result is a matrix with @code{length (@var{x})} rows and
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58 ## @code{length (@var{alpha})} columns. Otherwise, @var{alpha} and
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59 ## @var{x} must conform and the result will be the same size.
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60 ##
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61 ## The value of @var{alpha} must be real. The value of @var{x} may be
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62 ## complex.
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63 ##
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64 ## If requested, @var{ierr} contains the following status information
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65 ## and is 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
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79 ## half of machine accuracy.
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80 ##
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81 ## @item
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82 ## Complete loss of significance by argument reduction, return @code{NaN}.
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83 ##
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84 ## @item
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85 ## Error---no computation, algorithm termination condition not met,
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86 ## return @code{NaN}.
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87 ## @end enumerate
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88 ## @end deftypefn
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89
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90 function bessel ()
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91 error ("bessel: you must use besselj, bessely, besseli, or besselk");
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92 endfunction
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93