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bessel

PURPOSE

% Compute Bessel or Hankel functions of various kinds:

function bessel

DESCRIPTION

```% -*- texinfo -*-
% @deftypefn {Loadable Function} {[@var{j}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt})
% @deftypefnx {Loadable Function} {[@var{y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})
% @deftypefnx {Loadable Function} {[@var{i}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})
% @deftypefnx {Loadable Function} {[@var{k}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})
% @deftypefnx {Loadable Function} {[@var{h}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt})
% Compute Bessel or Hankel functions of various kinds:
%
% @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 @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 @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 @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
% @code{exp (-I*@var{x})} for @var{k} = 1 or @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 value of @var{alpha} must be real.  The value of @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
% Complete loss of significance by argument reduction, return @code{NaN}.
% @item
% Error---no computation, algorithm termination condition not met,
% return @code{NaN}.
% @end enumerate
% @end deftypefn```

CROSS-REFERENCE INFORMATION

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