normalized ALF (Assotiated Legendre Function)

[Ben Abbott]

On Feb 12, 2008, at 1:44 AM, Dmitri A. Sergatskov wrote:

> FWIW: Marko's script seems to agree with "legendre_Plm"
> wrapper of GSL's function (gsl package from octave-forge).
>
> Sincerely,
>
> Dmitri.
> --


That is good news!

It would be nice to do a direct comparison for the example below.

	result_matlab = legendre (80, [-1:0.1:1]);

Any chance anyone who knows c/c++ has the inclination to write a short  
program using gsl to calculate that example and post the results?

In addition, I noticed the comment below in the reference manual for  
gsl,

"The following functions compute the associated Legendre Polynomials  
P_l^m(x). Note that this function grows combinatorially with l and can  
overflow for l larger than about 150. There is no trouble for small m,  
but overflow occurs when m and l are both large. Rather than allow  
overflows, these functions refuse to calculate P_l^m(x) and return  
GSL_EOVRFLW when they can sense that l and m are too big."

It would be more proper to restrict the issuing of the warning for the  
cases where overflow actually occurs. For example, even this trivial  
calculation warns of overflow.

	octave:73> legendre(0,0)
	warning: legendre is unstable for higher orders
	ans =  1

I'll take a look at modifying the script to catch overflows and issue  
the warning only when such occurs.

Ben
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