Re: Offer to help with TR1 Math

[Ed Smith-Rowland <3dw4rd at verizon dot net>]

Curt Brune wrote:
> On Tue, Nov 21, 2006 at 10:57:20PM -0500, Ed Smith-Rowland wrote:
>   
> > A fellow physicist!  I'm a nuke myself.  I would say the basics of what 
> > I said in that email are still true.
> > The biggest holes are still the Bessel and Neumann functions of 
> > arbitrary real order.  There is a scheme used by the GSL project and 
> > described in the second edition of Numerical Recipes that I think we'll 
> > adopt.
> >     
>
> I have that book and can look in to it.
>
>   
I used Arfken for the orthogonal polynomials (Legendre, Laguerre, Hermite).

I used Abramowitz and Stegun for just about everything.

> > The whole thing needs to be worked over for sanity and naming and 
> > commentary.
> >
> > Plus putting these functions through real use would really help.
> >
> > Anyhoo, help would be most welcome!  This material is, as one of my 
> > professors said, is "cut but not dried".  I guess that goes some way 
> > towards explaining why the C++ committee decided not to move these 
> > functions into the main C++ draft.
> >
> > *sniff*
> >
> > Anyway, maybe with another implementation the balance of power will 
> > shift . . .
> >     
>
> I am looking at
> http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf
>
> Is that what you use as the current draft?  I see Bessel and Neumann
> functions, just not of "arbitrary real order" -- is that your point?
> I'm just trying to get up to speed on the project status.
>
>   
The Bessel functions I was thinking of are in 5.2.1.8 through 5.2.1.11:

// [5.2.1.8] regular modified cylindrical Bessel functions:

double cyl_bessel_i(double nu, double x);

float cyl_bessel_if(float nu, float x);

long double cyl_bessel_il(long double nu, long double x);

// [5.2.1.9] cylindrical Bessel functions (of the first kind):

double cyl_bessel_j(double nu, double x);

float cyl_bessel_jf(float nu, float x);

long double cyl_bessel_jl(long double nu, long double x);

// [5.2.1.10] irregular modified cylindrical Bessel functions:

double cyl_bessel_k(double nu, double x);

float cyl_bessel_kf(float nu, float x);

long double cyl_bessel_kl(long double nu, long double x);

// [5.2.1.11] cylindrical Neumann functions;

// cylindrical Bessel functions (of the second kind):

double cyl_neumann(double nu, double x);

float cyl_neumannf(float nu, float x);

long double cyl_neumannl(long double nu, long double x);

This is a complication but OTOH, it makes the spherical Bessel functions trivial
because they are cylindrical bessel functions with nu = 1/2 times some crud.

Also, I was thinking that as a gnu extension we could provide
Airy functions which are linear combinations of Bessel functions of order 1/3.


> > I'll send what I have tomorrow after I make sure it doesn't crash.
> >
> >     
>
> OK.  Great.
>
>