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Showing that a hypergeometric expression is 0?
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