A combinatorial sum with two complex parameters

Abstract

This article deals with combinatorial identities with two complex parameters. Starting with a fundamental lemma, we derive various polynomial identities, combinatorial sums and related results. For example, we generalize a polynomial identity of Carlitz involving central binomial coefficients and present a second identity of the same nature. Special cases of our findings lead to sums involving Catalan numbers, harmonic numbers, and Fibonacci numbers.