Combinatorial proofs of identities in basic hypergeometric series

Combinatorial proofs of identities in basic hypergeometric series

In this paper, the q–Pfaff-Saalschütz formula and the q–Sheppard 3φ2 transformation formula are established combinatorially.

Combinatorial Proofs of q-Series Identities

We provide combinatorial proofs of six of the ten q-series identities listed in [3, Theorem 3]. Andrews, Jiménez-Urroz and Ono prove these identities using formal manipulation of identities arising in the theory of basic hypergeometric series. Our proofs are purely combinatorial, based on interpreting both sides of the identities as generating functions for certain partitions. One of these iden...

Elementary Derivations of Identities for Bilateral Basic Hypergeometric Series

We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof (“A simple proof of Bailey’s very-well-poised 6ψ6 summation”, Proc. Amer. Math. Soc., to appear) of Bailey’s very-well-poised 6ψ6 summation. Using a similar but different method, we now gi...

2 00 1 Combinatorial proofs of q - series identities

Basic Hypergeometric Series

Abstract. We compute the inverse of a specific infinite r-dimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an r-dimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite r-dimensional matrix. As applications of our matrix inversions, we derive ...