Re: [Bug-gsl] Confluent Hypergeometric 1F1 request

[Raymond Rogers]

On 10/02/2014 02:16 PM, Patrick Alken wrote:
> On 10/02/2014 12:11 PM, Raymond Rogers wrote:
> > I believe I have found some problems and perhaps a solution in the 
> > 1F1 code.
> > Could somebody (s) evaluate the following in Maple and Mathematica and
> > post the results?
> > 1F1( -1, -2, -4)
> >
> > The online Mathematica answer is: -1.000000000000000000000
> > Whereas GSL gives 0.0549469166662
> >
> > If anybody is willing to discuss the calculation details; I would be
> > grateful.   I have reached a conclusion that should be double checked.
> >
> > Ray
> My mathematica says -1.
Let me give a short form of why GSL (and some other algorithms) go wrong.
Let b<a<0  be negative integers.  Then we have a finite sum (polynomial) 
if x>0  or x<0 .  But in order to avoid certain calculation probems ; if 
x<0 Kummers transform is applied M(a,b,x)=e^x M(b-a,b,-x)  .  Notice 
that b<(b-a)<0 afterwards so the same summation is applied to M(b-a,b,x) 
yielding another polynomial.
But if this were valid we could say.
e^x  =  ratio of two polynomials; which isn't true.


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