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From: | Raymond Rogers |
Subject: | Re: [Bug-gsl] Confluent Hypergeometric 1F1 request |
Date: | Thu, 02 Oct 2014 18:30:06 -0400 |
User-agent: | Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.1.1 |
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. RayMy 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. -- The primary use of conversation is to satisfy the impulse to talk George Santanyana
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