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Showing that a hypergeometric expression is 0?

• To: mathgroup at smc.vnet.net
• Subject: [mg73277] Showing that a hypergeometric expression is 0?
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Fri, 9 Feb 2007 02:26:15 -0500 (EST)

How can I use Mathematica to show that

n Hypergeometric2F1Regularized[k, 1 - n, 1 + k - n, -1] +
Hypergeometric2F1Regularized[k, -n, k - n, -1] +
k n Hypergeometric2F1Regularized[1 + k, 1 - n, 2 + k - n, -1] -
k Hypergeometric2F1Regularized[1 + k, -n, 1 + k - n, -1]

is identically 0?

I presume that I could do that by hand, perhaps without much trouble. But I
also have far, far messier expressions involving hypergeometric functions
which I need to show to be identically 0, and I really don't want to have
to do so by hand!

David W. Cantrell