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Название: Summation of Binomial Coefficients Using Hypergeometric Functions
Авторы: Hayden M.B., Lamagna E.A.
An algorithm which finds the definite sum of many series involving binomial coefficients b presented. The method examines the ratio of two consecutive terms of the series in an attempt to express the sum as an ordinary hypergeometric function. A closed form for the infinite sum may b* found by comparing the resulting function with known summation theorems. It may also be possible to identify ranges of the summation index for which summing to a finite upper limit is the same as summing to infinity.