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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


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