Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.7

On the Binomial Identities of Frisch and Klamkin

H. W. Gould
Department of Mathematics
West Virginia University
Morgantown, WV 26506

Jocelyn Quaintance
Department of Computer Science
University of Pennsylvania
Philadelphia, PA 19104


In this paper we investigate two somewhat similar identities for sums of ratios of binomial coefficients. We give several proofs, and note that the identities all follow from a hypergeometric identity of Gauss. Inverse identities are also given.

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Received July 4 2016; revised versions received August 31 2016; September 1 2016; September 7 2016. Published in Journal of Integer Sequences, September 7 2016.

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