1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
|
########################################################################
##
## Copyright (C) 1996-2022 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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 <you must use besselj, ...> bessel ()
|
