ISSN:
1572-9303
Keywords:
multiple basic hypergeometric series related to the root systems An
;
Cn and Dn
;
U(n + 1) series
;
q-Pfaff-Saalschütz sum
;
very-well-poised 6φ5 sum
;
q-Gauss summation
;
q-Whipple transformation
;
q-Dougall sum
;
Rogers-Selberg function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We study multiple series extensions of basic hypergeometric series related to the root system Dn. We make a small change in the notation used for Cn and Dn series to bring them closer to An series. This allows us to combine the three types of series, and get Dn extensions of the following classical summation and transformation theorems: The q-Pfaff-Saalschütz summation, Rogers' 6 φ5 sum, the q-Gauss summation, q-Chu-Vandermonde summations, Watson's q-analogue of Whipple's transformation, and the q-Dougall summation theorem. We also define An and Cn extensions of the Rogers-Selberg function, and prove a reduction formula for both of them. This generalizes some work of Andrews. We use some techniques originally developed to study multiple basic hypergeometric series related to the root system An (U(n + 1) basic hypergeometric series).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006997424561
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