SEVERAL GENERALIZATIONS AND VARIATIONS OF CHU-VANDERMONDE IDENTITY

Abstract

In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach to the expressions for the k-th moments ($k=1,2$) of some particular cases of investigated discrete random variables by the author of this paper [16]. As applications of one of these Chu-Vandermonde-type identities, we prove two congruences modulo $P^4$ and modulo $P^5$, , where p ≥ 5 is a prime number.