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arXiv · 2608.05192

Extensions of several famous combinatorial identities via hypergeometric functions

Arjun Kumar Rathie·Feng Qi·Dongkyu Lim
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Abstract

The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.

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Arjun Kumar Rathie, Feng Qi, Dongkyu Lim. 2026-08-03. Extensions of several famous combinatorial identities via hypergeometric functions. https://arxiv.org/abs/2608.05192

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