8 Aug
2013
8 Aug
'13
4:48 p.m.
After catching up on sleep I'll doubtless regret sending this, but while I was fooling with alternating binomial sums, Mma unsimplified one of them, resulting in HypergeometricPFQ[{1,1/2-n+Floor[n/2],1-n+Floor[n/2]},{3/2+Floor[n/2],2+Floor[n/2]},1]== ((4^n-(-1)^n Binomial[2 n,n]) Gamma[2 n-2 Floor[n/2]] Gamma[3+2 Floor[n/2]])/(2 Gamma[2+2 n]), integer n >0. It might be something simple that got bisected and reversed, but it seems a bit too exotic. Macsyma did it with Dixon's thm, but only after I separated the even and odd cases. Why didn't Mma? --rwg