Gauss's 2F1(1) cannot be generalized to 2F1(x),

By Doron Zeilberger.

Appeared in J. Comp. Appl. Math. 39 (1992) 379-382 .

Petkovsek's famous algorithm can always decide about the close-formness of a hypergemetric sum, but if you have at least one extra parameter, you can often prove it directly, using asymptotics.

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