specfunc-bessel.texi

用于VC.net的gsl的lib库文件包

@cindex Bessel functions

The routines described in this section compute the Cylindrical Bessel
functions @math{J_n(x)}, @math{Y_n(x)}, Modified cylindrical Bessel
functions @math{I_n(x)}, @math{K_n(x)}, Spherical Bessel functions
@math{j_l(x)}, @math{y_l(x)}, and Modified Spherical Bessel functions
@math{i_l(x)}, @math{k_l(x)}.  For more information see Abramowitz & Stegun,
Chapters 9 and 10.  The Bessel functions are defined in the header file
@file{gsl_sf_bessel.h}.

@menu
* Regular Cylindrical Bessel Functions::  
* Irregular Cylindrical Bessel Functions::  
* Regular Modified Cylindrical Bessel Functions::  
* Irregular Modified Cylindrical Bessel Functions::  
* Regular Spherical Bessel Functions::  
* Irregular Spherical Bessel Functions::  
* Regular Modified Spherical Bessel Functions::  
* Irregular Modified Spherical Bessel Functions::  
* Regular Bessel Function - Fractional Order::  
* Irregular Bessel Functions - Fractional Order::  
* Regular Modified Bessel Functions - Fractional Order::  
* Irregular Modified Bessel Functions - Fractional Order::  
* Zeros of Regular Bessel Functions::  
@end menu

@node Regular Cylindrical Bessel Functions
@subsection Regular Cylindrical Bessel Functions
@cindex Cylindrical Bessel Functions
@cindex Regular Cylindrical Bessel Functions

@deftypefun double gsl_sf_bessel_J0 (double @var{x})
@deftypefunx int gsl_sf_bessel_J0_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular cylindrical Bessel function of zeroth
order, @math{J_0(x)}.
@comment Exceptional Return Values: none
@end deftypefun

@deftypefun double gsl_sf_bessel_J1 (double @var{x})
@deftypefunx int gsl_sf_bessel_J1_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular cylindrical Bessel function of first
order, @math{J_1(x)}.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_Jn (int @var{n}, double @var{x})
@deftypefunx int gsl_sf_bessel_Jn_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular cylindrical Bessel function of 
order @var{n}, @math{J_n(x)}.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_Jn_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the regular cylindrical Bessel
functions @math{J_n(x)} for @math{n} from @var{nmin} to @var{nmax}
inclusive, storing the results in the array @var{result_array}.  The
values are computed using recurrence relations, for efficiency, and
therefore may differ slightly from the exact values.
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun


@node Irregular Cylindrical Bessel Functions
@subsection Irregular Cylindrical Bessel Functions
@cindex Irregular Cylindrical Bessel Functions

@deftypefun double gsl_sf_bessel_Y0 (double @var{x})
@deftypefunx int gsl_sf_bessel_Y0_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular cylindrical Bessel function of zeroth
order, @math{Y_0(x)}, for @math{x>0}.
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_Y1 (double @var{x})
@deftypefunx int gsl_sf_bessel_Y1_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular cylindrical Bessel function of first
order, @math{Y_1(x)}, for @math{x>0}.
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_Yn (int @var{n},double @var{x})
@deftypefunx int gsl_sf_bessel_Yn_e (int @var{n},double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular cylindrical Bessel function of 
order @var{n}, @math{Y_n(x)}, for @math{x>0}.
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_Yn_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the irregular cylindrical Bessel
functions @math{Y_n(x)} for @math{n} from @var{nmin} to @var{nmax}
inclusive, storing the results in the array @var{result_array}.  The
domain of the function is @math{x>0}.  The values are computed using
recurrence relations, for efficiency, and therefore may differ slightly
from the exact values.
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun


@node Regular Modified Cylindrical Bessel Functions
@subsection Regular Modified Cylindrical Bessel Functions
@cindex Modified Cylindrical Bessel Functions
@cindex Regular Modified Cylindrical Bessel Functions

@deftypefun double gsl_sf_bessel_I0 (double @var{x})
@deftypefunx int gsl_sf_bessel_I0_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular modified cylindrical Bessel function
of zeroth order, @math{I_0(x)}.
@comment Exceptional Return Values: GSL_EOVRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_I1 (double @var{x})
@deftypefunx int gsl_sf_bessel_I1_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular modified cylindrical Bessel function
of first order, @math{I_1(x)}.
@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_In (int @var{n}, double @var{x})
@deftypefunx int gsl_sf_bessel_In_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular modified cylindrical Bessel function
of order @var{n}, @math{I_n(x)}.
@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_In_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the regular modified cylindrical
Bessel functions @math{I_n(x)} for @math{n} from @var{nmin} to
@var{nmax} inclusive, storing the results in the array
@var{result_array}.  The start of the range @var{nmin} must be positive
or zero.  The values are computed using recurrence relations, for
efficiency, and therefore may differ slightly from the exact values.
@comment Domain: nmin >=0, nmax >= nmin 
@comment Conditions: n=nmin,...,nmax, nmin >=0, nmax >= nmin 
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_I0_scaled (double @var{x})
@deftypefunx int gsl_sf_bessel_I0_scaled_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled regular modified cylindrical Bessel
function of zeroth order @math{\exp(-|x|) I_0(x)}.
@comment Exceptional Return Values: none
@end deftypefun

@deftypefun double gsl_sf_bessel_I1_scaled (double @var{x})
@deftypefunx int gsl_sf_bessel_I1_scaled_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled regular modified cylindrical Bessel
function of first order @math{\exp(-|x|) I_1(x)}.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_In_scaled (int @var{n}, double @var{x})
@deftypefunx int gsl_sf_bessel_In_scaled_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled regular modified cylindrical Bessel
function of order @var{n}, @math{\exp(-|x|) I_n(x)} 
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_In_scaled_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the scaled regular cylindrical
Bessel functions @math{\exp(-|x|) I_n(x)} for @math{n} from
@var{nmin} to @var{nmax} inclusive, storing the results in the array
@var{result_array}. The start of the range @var{nmin} must be positive
or zero.  The values are computed using recurrence relations, for
efficiency, and therefore may differ slightly from the exact values.
@comment Domain: nmin >=0, nmax >= nmin 
@comment Conditions:  n=nmin,...,nmax 
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun


@node Irregular Modified Cylindrical Bessel Functions
@subsection Irregular Modified Cylindrical Bessel Functions
@cindex Irregular Modified Cylindrical Bessel Functions

@deftypefun double gsl_sf_bessel_K0 (double @var{x})
@deftypefunx int gsl_sf_bessel_K0_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular modified cylindrical Bessel
function of zeroth order, @math{K_0(x)}, for @math{x > 0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_K1 (double @var{x})
@deftypefunx int gsl_sf_bessel_K1_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular modified cylindrical Bessel
function of first order, @math{K_1(x)}, for @math{x > 0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_Kn (int @var{n}, double @var{x})
@deftypefunx int gsl_sf_bessel_Kn_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the irregular modified cylindrical Bessel
function of order @var{n}, @math{K_n(x)}, for @math{x > 0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_Kn_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the irregular modified cylindrical
Bessel functions @math{K_n(x)} for @math{n} from @var{nmin} to
@var{nmax} inclusive, storing the results in the array
@var{result_array}. The start of the range @var{nmin} must be positive
or zero. The domain of the function is @math{x>0}. The values are
computed using recurrence relations, for efficiency, and therefore
may differ slightly from the exact values.
@comment Conditions: n=nmin,...,nmax 
@comment Domain: x > 0.0, nmin>=0, nmax >= nmin
@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_K0_scaled (double @var{x})
@deftypefunx int gsl_sf_bessel_K0_scaled_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled irregular modified cylindrical Bessel
function of zeroth order @math{\exp(x) K_0(x)} for @math{x>0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM
@end deftypefun

@deftypefun double gsl_sf_bessel_K1_scaled (double @var{x}) 
@deftypefunx int gsl_sf_bessel_K1_scaled_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled irregular modified cylindrical Bessel
function of first order @math{\exp(x) K_1(x)} for @math{x>0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_Kn_scaled (int @var{n}, double @var{x})
@deftypefunx int gsl_sf_bessel_Kn_scaled_e (int @var{n}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the scaled irregular modified cylindrical Bessel
function of order @var{n}, @math{\exp(x) K_n(x)}, for @math{x>0}.
@comment Domain: x > 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_Kn_scaled_array (int @var{nmin}, int @var{nmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the scaled irregular cylindrical
Bessel functions @math{\exp(x) K_n(x)} for @math{n} from @var{nmin} to
@var{nmax} inclusive, storing the results in the array
@var{result_array}. The start of the range @var{nmin} must be positive
or zero.  The domain of the function is @math{x>0}. The values are
computed using recurrence relations, for efficiency, and therefore
may differ slightly from the exact values.
@comment Domain: x > 0.0, nmin >=0, nmax >= nmin 
@comment Conditions: n=nmin,...,nmax 
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun


@node Regular Spherical Bessel Functions
@subsection Regular Spherical Bessel Functions
@cindex Spherical Bessel Functions
@cindex Regular Spherical Bessel Functions

@deftypefun double gsl_sf_bessel_j0 (double @var{x})
@deftypefunx int gsl_sf_bessel_j0_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular spherical Bessel function of zeroth
order, @math{j_0(x) = \sin(x)/x}.
@comment Exceptional Return Values: none
@end deftypefun

@deftypefun double gsl_sf_bessel_j1 (double @var{x})
@deftypefunx int gsl_sf_bessel_j1_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular spherical Bessel function of first
order, @math{j_1(x) = (\sin(x)/x - \cos(x))/x}.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_j2 (double @var{x})
@deftypefunx int gsl_sf_bessel_j2_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular spherical Bessel function of second
order, @math{j_2(x) = ((3/x^2 - 1)\sin(x) - 3\cos(x)/x)/x}.
@comment Exceptional Return Values: GSL_EUNDRFLW
@end deftypefun

@deftypefun double gsl_sf_bessel_jl (int @var{l}, double @var{x})
@deftypefunx int gsl_sf_bessel_jl_e (int @var{l}, double @var{x}, gsl_sf_result * @var{result})
These routines compute the regular spherical Bessel function of 
order @var{l}, @math{j_l(x)}, for @c{$l \geq 0$}
@math{l >= 0} and @c{$x \geq 0$}
@math{x >= 0}.
@comment Domain: l >= 0, x >= 0.0 
@comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW
@end deftypefun

@deftypefun int gsl_sf_bessel_jl_array (int @var{lmax}, double @var{x}, double @var{result_array}[])
This routine computes the values of the regular spherical Bessel
functions @math{j_l(x)} for @math{l} from 0 to @var{lmax}
inclusive  for @c{$lmax \geq 0$}
@math{lmax >= 0} and @c{$x \geq 0$}
@math{x >= 0}, storing the results in the array @var{result_array}.
The values are computed using recurrence relations, for
efficiency, and therefore may differ slightly from the exact values.