Re: Bug in Mathematica 7.0?
- To: mathgroup at smc.vnet.net
- Subject: [mg99130] Re: Bug in Mathematica 7.0?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Tue, 28 Apr 2009 04:43:43 -0400 (EDT)
- Organization: Uni Leipzig
- References: <gt3tla$non$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi,
a) Gamma[] allow non integer arguments
b) Product[Gamma[M + j]*Gamma[1/2 + j]*
Gamma[r + 1/2 + j]/Gamma[r + M + j], {j, 0,
M - 1}]
gives already an expression in terms of Barnes G function
bu a different form yours. So it is no wonder that the results
for inserted numbers are not the same.
So, either Mathematica's symbolic product algorithms may be
wrong your our algebra.
Regards
Jens
Not An Expert wrote:
> Hello Mathematica-Experts,
>
> I'm using Mathematica 7.0 on a Windows XP machine and might have come across
> a bug in Mathematica 7.0.
>
> I define the following function as a product of Gamma functions:
>
> A[M_, r_] := Product[Gamma[M + j]*Gamma[1/2 + j]*Gamma[r + 1/2 + j]/
> Gamma[r + M + j], {j, 0, M - 1}]
>
> To allow non-integer values M we re-write the above expression in terms
> of the Barnes G-function and so we obtain (we've checked the algebra
> many times!):
>
> B[M_, r_] := BarnesG[2 + M]/BarnesG[2]*BarnesG[1/2 + M]/BarnesG[1/2]
> *BarnesG[r + 1/2 + M]/
> BarnesG[r + 1/2]*BarnesG[r + M]/BarnesG[r + 2*M]
>
> As a test I've chosen M = 2 and r = 1
> and indeed I obtain
> A[2, 1] = Pi^2/32
> and
> B[2, 1] = Pi^2/32
> and so agreement in both functions.
>
> But choosing M = 3 and r = 1 gives
> A[3, 1] = 9*Pi^3/2048
> B[3, 1] = 3^Pi^3/16384
>
> So two different values for A[3, 1] and B[3, 1].
> Also A[3, 0] and B[3, 0] would give different answers - and there are
> many other examples.
>
> Do you have any thoughts on what went wrong?
>
> Cheerio!
>