[Maxima] big float gamma

Viktor T. Toth vttoth at vttoth.com
Thu Sep 6 08:23:27 CDT 2007


Actually, I think bffac is correct; just keep in mind that it is the
extended factorial, not gamma (i.e., Gamma(z) = bffac(z - 1)):

(%i8) abs(rectform(bffac(-5.0*%i-1,16)));
(%o8)                        4.351751096374172b-4


Viktor
 

-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Raymond Toy (RT/EUS)
Sent: Thursday, September 06, 2007 8:29 AM
To: Barton Willis
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] big float gamma

Barton Willis wrote:
> In bffac.mac, there is a big float gamma function bffac (author Bill
> Gosper).
> I was testing this function with complex inputs -- the output isn't in
> rectangular form (it's a big mess). So I was wondering: Is bffac
> algorithmically
> correct for (all) complex inputs? If so, maybe we could insert some calls
> to rectform
> into the code? Example:
> 
> (%i49) float2bf : true$
> (%i50) load(bffac)$
> 
> (%i51) bffac(-5.0 + %i,25);
> 
> < long mess deleted >
> 
> (%i52) rectform(%);
> (%o52) 1.262948529867786b-2-7.163743828758051b-4*%i
> 
A&S says abs(gamma(%i*y)) = sqrt(%pi/(y*sinh(%pi*y)).

abs(rectform(bffac(5b0*%i,16))) -> 2.175875548187084b-3

But it should be  4.3517510963741685e-4

And gamma(5.0*%i) -> 3.399328988721385e-4 %i - 2.717038835061503e-4, 
which has the magnitude  4.3517510963741857e-4.

Seems like bffac is not correct for complex args.

Ray
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