Generalizations of Milne's $U(n+1)$ $q$-Chu-Vandermonde summation

Fang, Jian-Ping

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 395-407

Abstract (VO)

We derive two identities for multiple basic hyper-geometric series associated with the unitary $U(n+1)$ group. In order to get the two identities, we first present two known $q$-exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two $U(n+1)$ $q$-Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial coefficients. In addition, we also derive two nontrivial summation equations from the two multiple extensions.

Détail

DOI : 10.1007/s10587-016-0263-0

Classification : 11B65, 15A09, 33C80, 33D70, 33D80
Keywords: $U(n+1)$ group; multiple basic hypergeometric series; basic hypergeometric series

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