q-Hypergeometric Series and Macdonald Functions

A one-parameter rational function generalisation Rλ(X;b) of the symmetric Macdonald polynomial and interpolation Macdonald polynomial is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal ...

The main object of this paper is to present a systematic investigation of various families of generating functions and other related results involving hypergeometric and q-hypergeometric polynomials. The authors especially consider several general ...

We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series,...