On certain multiple Bailey, Rogers and Dougall type summation formulas

Details On certain multiple Bailey, Rogers and Dougall type summation formulas On certain multiple Bailey, Rogers and Dougall type summation formulas

1997-12-25

arxiv.org/abs/math/9712265v1

Publ. Res. Inst. Math. Sci. 33 (1997), 483-508

Mathematics

Combinatorics

20 pages, LaTeX

Scientific paper

10.2977/prims/1195145326

A multidimensional generalization of Bailey's very-well-poised bilateral basic hypergeometric ${}_6\psi_6$ summation formula and its Dougall type ${}_5H_5$ hypergeometric degeneration for $q\to 1$ is studied. The multiple Bailey sum amounts to an extension corresponding to the case of a nonreduced root system of certain summation identities associated to the reduced root systems that were recently conjectured by Aomoto and Ito and proved by Macdonald. By truncation, we obtain multidimensional analogues of the very-well-poised unilateral (basic) hypergeometric Rogers ${}_6\phi_5$ and Dougall ${}_5F_4$ sums (both nonterminating and terminating). The terminating sums may be used to arrive at product formulas for the norms of recently introduced ($q$-)Racah polynomials in several variables.

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