normalized ALF (Assotiated Legendre Function)

[Ben Abbott]

I've added a check for underflow. This is my first time doing such, so  
I may be quite off on what is commonly accepted as proper.

The method I used detects an underflow for orders greater than 151.

	octave:104> result_octave1 = legendre  (152, [-1:0.1:1]);
	warning: legendre: results may be  unstable for high orders.

I've attached the script.

Ben

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On Feb 12, 2008, at 1:38 PM, Ben Abbott wrote:

> On Tuesday, February 12, 2008, at 10:02AM, "Marco Caliari" <marco.caliari at univr.it 
> > wrote:
>> Hi.
>>
>> The normalized Lagrange functions should (almost) never give NaNs  
>> of Infs.
>> The enclosed script fixes a problem in the previous:
>>
>> octave:1> legendreold(151,-0.9,"norm")(end-1:end)
>> ans =
>>
>>  -3.3248e-53
>>          Inf
>> octave:2> legendre(151,-0.9,"norm")(end-1:end)
>> ans =
>>
>>  -3.3248e-53
>>   9.2660e-55
>>
>> Marco
>>
>
> I've tried to combine the various implementations. I still need to  
> look into adding a warning in then event of an overflow.
>
> We should also add more tests to include the current improvements.
>
> Ben
>
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