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[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!

**Follow-Ups**:**Re: Bug in Mathematica 7.0?***From:*Daniel Lichtblau <danl@wolfram.com>