       Bug in Mathematica 7.0?

• To: mathgroup at smc.vnet.net
• Subject: [mg99116] Bug in Mathematica 7.0?
• From: Not An Expert <not_an_expert at directbox.com>
• Date: Mon, 27 Apr 2009 05:25:02 -0400 (EDT)

```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*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!

```

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