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.