I've been attempting to calculate Bessel's functions to work up a new syntax
(fortran95), believing that when I had a good guess, I would simply be able
to find some table out there on the net to compare it to.
[cut]
total = 0.34693

Is .35 J(7) of the fifth order?

On Thu, 8 Mar 2007, Lane Straatman wrote:

I've been attempting to calculate Bessel's functions to work up a new
syntax
(fortran95), believing that when I had a good guess, I would simply be
able
to find some table out there on the net to compare it to.
[cut]
total = 0.34693

Is .35 J(7) of the fifth order?

Approximately, but not exactly. J5(7) = 0.34790 is the correct value to 5
sig figs. Abramowitz and Stegun (which you can find online) gives tables
of Bessel functions; this particular value is on page 398 (10th printing).
Well that's exciting as all get out. I usually have to get a few offensive

You will find that Bessel functions generally are categorized by type
and order.
This is the interface to the Cephes library (C routines) for Bessel
functions:

extern double i0(double x);
extern double i0e(double x);
extern double i1(double x);
extern double i1e(double x);
extern double iv(double v,double x);
extern double j0(double x);
extern double j1(double x);
extern double jn(int n,double x);
extern double jv(double n,double x);
extern double k0(double x);
extern double k0e(double x);
extern double k1(double x);
extern double k1e(double x);
extern double kn(int nn,double x);
extern double y0(double x);
extern double y1(double x);
extern double yn(int n,double x);

I guess that most Fortran libraries will be very similar.
I was going to do this in C, but decided that my knowledge of types was

total = 0.3478969633579254
This agrees with Timo's five sig figs, and I wouldn't be surprised if there
are 15 sig figs there. Finding these things on the net is killing me.
Everywhere looks like this:
http://www.math.sfu.ca/~cbm/aands/frameindex.htm
Is there a .pdf out there of these data so I can see it without it looking
like trying to read a technical journal with a telescope?

On Fri, 9 Mar 2007 17:43:36 -0500, "Lane Straatman"
invalid@invalid.net> wrote:

[snip]

total = 0.3478969633579254
This agrees with Timo's five sig figs, and I wouldn't be surprised if there
are 15 sig figs there. Finding these things on the net is killing me.
Everywhere looks like this:
http://www.math.sfu.ca/~cbm/aands/frameindex.htm
Is there a .pdf out there of these data so I can see it without it looking
like trying to read a technical journal with a telescope?

You can at least spot-check values using Mathematica at the Wolfram
Functions Site,
http://functions.wolfram.com/

For BesselJ, link here then click Evaluation.
http://functions.wolfram.com/BesselAiryStruveFunctions/BesselJ/

J5(7), to 20D, gives 0.34789632475118328514

HTH

If you do it in double precision you can match the number above to 15

"Timo Nieminen" <timo@physics.uq.edu.au> wrote:
On Thu, 8 Mar 2007, Lane Straatman wrote:

I've been attempting to calculate Bessel's functions to work up a new
syntax
(fortran95), believing that when I had a good guess, I would simply be
able
to find some table out there on the net to compare it to.
[cut]
total = 0.34693

Is .35 J(7) of the fifth order?

Approximately, but not exactly. J5(7) = 0.34790 is the correct value to 5
sig figs. Abramowitz and Stegun (which you can find online) gives tables
of Bessel functions; this particular value is on page 398 (10th printing).
Well that's exciting as all get out. I usually have to get a few offensive
rebounds before I score. I've got to figure out how to calculate the
higher-order terms without busting datatypes, and then I think I've got it.

On Fri, 9 Mar 2007, Lane Straatman wrote:

"Timo Nieminen" <timo@physics.uq.edu.au> wrote:
On Thu, 8 Mar 2007, Lane Straatman wrote:

I've been attempting to calculate Bessel's functions to work up a new
syntax
(fortran95), believing that when I had a good guess, I would simply be
able
to find some table out there on the net to compare it to.
[cut]
total = 0.34693

Is .35 J(7) of the fifth order?

Approximately, but not exactly. J5(7) = 0.34790 is the correct value to
5
sig figs. Abramowitz and Stegun (which you can find online) gives
tables
of Bessel functions; this particular value is on page 398 (10th
printing).
Well that's exciting as all get out. I usually have to get a few
offensive
rebounds before I score. I've got to figure out how to calculate the
higher-order terms without busting datatypes, and then I think I've got
it.

Avoid factorials. Factorials will kill the algorithm, for large n. For
quite a few special functions, there are explicit formulae that involve
factorials. OK for small n, but useless in practice for large n. Use
recursion formulae instead. Alas, these can be unstable for certain
ranges.
I'm using factorial instead of the gamma function. It occurs to me that I

Badger wrote:

If you do it in double precision you can match the number above to 15
significant digits
i.e. dbl precision version-
program bessel7
IMPLICIT NONE
real(, external :: factorial
With small changes to what you wrote, I'm able to get fifteen places:

#include <math.h
#include "specfunc/gsl_sf_gamma.h"
#include "specfunc/gsl_sf_hyperg.h"
What do these look like? I'm unusually interested in something that will

double jaz(double alpha, double zeta)
{
double half_z = zeta * 0.5;
double ap1 = alpha + 1.0;
return (pow(half_z, alpha) / gsl_sf_gamma(ap1)) *
gsl_sf_hyperg_0F1(ap1, -(half_z * half_z));
}

#ifdef UNIT_TEST
#include <stdio.h
int main(void)
{
double alpha;
double zeta;
double result = 0;
unsigned a,
z;
for (a = 0; a < 10; a++)
for (z = 0; z < 10; z++) {
alpha = a;
zeta = z;
result = jaz(alpha, zeta);
printf("J%u(%u) = %25.18g\n", a, z, result);
}
return 0;
}
What happens to the above when your gamma function hands it something that

J0(0) = 1
One should be able to say why this is so a priori.

"user923005" <dcorbit@connx.com> wrote in message
news:1173504818.565719.11700@h3g2000cwc.googlegroups.com...
#include <math.h
#include "specfunc/gsl_sf_gamma.h"
#include "specfunc/gsl_sf_hyperg.h"
What do these look like? I'm unusually interested in something that will
allow me to calculate a gamma function robustly.

"user923005" <dcorbit@connx.com> wrote in message
news:1173504818.565719.11700@h3g2000cwc.googlegroups.com...
#include <math.h
#include "specfunc/gsl_sf_gamma.h"
#include "specfunc/gsl_sf_hyperg.h"
What do these look like? I'm unusually interested in something that will
allow me to calculate a gamma function robustly.