Macdonald Polynomials and Multivariable Basic Hypergeometric Series

We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised ${}_6\phi_5$ summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised ${}_8\phi_7$ summation. Motivated by our basic hypergeometric analysis, we propose an extension of Macdonald polynomials to Macdonald symmetric functions indexed by partitions with complex parts. These appear to possess nice properties.