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1 ## Copyright (C) 1996, 1997, 1999, 2000, 2005, 2007 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. |
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30 ## @item bessely |
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31 ## Bessel functions of the second kind. |
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32 ## @item besseli |
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33 ## Modified Bessel functions of the first kind. |
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34 ## @item besselk |
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35 ## Modified Bessel functions of the second kind. |
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36 ## @item besselh |
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37 ## Compute Hankel functions of the first (@var{k} = 1) or second (@var{k} |
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38 ## = 2) kind. |
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39 ## @end table |
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40 ## |
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41 ## If the argument @var{opt} is supplied, the result is scaled by the |
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42 ## @code{exp (-I*@var{x})} for @var{k} = 1 or @code{exp (I*@var{x})} for |
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43 ## @var{k} = 2. |
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44 ## |
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45 ## If @var{alpha} is a scalar, the result is the same size as @var{x}. |
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46 ## If @var{x} is a scalar, the result is the same size as @var{alpha}. |
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47 ## If @var{alpha} is a row vector and @var{x} is a column vector, the |
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48 ## result is a matrix with @code{length (@var{x})} rows and |
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49 ## @code{length (@var{alpha})} columns. Otherwise, @var{alpha} and |
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50 ## @var{x} must conform and the result will be the same size. |
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51 ## |
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52 ## The value of @var{alpha} must be real. The value of @var{x} may be |
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53 ## complex. |
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54 ## |
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55 ## If requested, @var{ierr} contains the following status information |
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56 ## and is the same size as the result. |
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57 ## |
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58 ## @enumerate 0 |
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59 ## @item |
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60 ## Normal return. |
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61 ## @item |
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62 ## Input error, return @code{NaN}. |
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63 ## @item |
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64 ## Overflow, return @code{Inf}. |
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65 ## @item |
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66 ## Loss of significance by argument reduction results in less than |
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67 ## half of machine accuracy. |
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68 ## @item |
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69 ## Complete loss of significance by argument reduction, return @code{NaN}. |
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70 ## @item |
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71 ## Error---no computation, algorithm termination condition not met, |
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72 ## return @code{NaN}. |
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73 ## @end enumerate |
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74 ## @end deftypefn |
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75 |
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76 function bessel () |
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77 error ("bessel: you must use besselj, bessely, besseli, or besselk"); |
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78 endfunction |
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79 |
