normalized ALF (Assotiated Legendre Function)

[Ben Abbott]

On Feb 11, 2008, at 3:01 AM, kruvalig wrote:

> Thank's a lot for quick answer. I very suprised of it.
>
> On Sun, 10 Feb 2008 01:37:10 +0300, Ben Abbott <bpabbott at mac.com>  
> wrote:
>
>> I've posted a patch and changelog to the maintainers list. Attached  
>> to
>> this
>> email is the modified script.
>> http://www.nabble.com/file/p15391002/legendre.m legendre.m
>
> Can any one test output of this file and output matlab file to high  
> degree
> (>70).
>
>   result_mlab=legendre(80,[-1:0.1:1], "norm");
>   result_octave=legendre(80,[-1:0.1:1], "norm");
>   max(max(abs(result_mlab-result_octave)))

	warning: legendre is unstable for higher orders
	ans =  1.4343e+16

This is what I get.

> Here ftp://77.108.213.161/result_octave_80 is a file, generated in  
> octave
> by code:
>
>   result_octave=legendre(80,[-1:0.1:1], "norm");
>   save -v7 result_octave_80
>
> I think this code
>   scale = (-1).^m .* sqrt ((n+0.5) .* factorial (n-m) ./ factorial (n 
> +m));
> whill give bad answer in high order of legendre.
> And we have to write: To what order it compute in right.

I'm not so sure a problem lies with the normalization. When I compare  
results for legendre(80, [-1:0.1:1]), I get

	warning: legendre is unstable for higher orders
	ans =  5.4154e+126

I haven't looked into the details as how this function works yet. I'll  
do that today.

In any event, can you (someone else?) propose a change? ... or a  
reference for how it should be done?

Ben