ISSN:
1432-0940
Keywords:
Key words. Multiple basic hypergeometric series associated to root systems An , Cn , and Dn , Jackson's 8φ7 summations, Terminating 10φ9 transformations, Watson's transformations, Sears' 4φ3 transformations, Heine's 2φ1 transformation, q -Gauss summation, q -Binomial theorem. AMS Classification. Primary 33D70; Secondary 05A19, 33D20.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. In this paper we derive multivariable generalizations of Bailey's classical terminating balanced very-well-poised 10 $\reallyphi$ 9 transformation. We work in the setting of multiple basic hypergeometric series very-well-poised on the root systems A n , C n , and D n . Following the distillation of Bailey's ideas by Gasper and Rahman [11], we use a suitable interchange of multisums. We obtain C n and D n 10 $\reallyphi$ 9 transformations combined with A n , C n , and D n extensions of Jackson's 8 $\reallyphi$ 7 summation. Milne and Newcomb have previously obtained an analogous formula for A n series. Special cases of our 10 $\reallyphi$ 9 transformations include several new multivariable generalizations of Watson's transformation of an 8 $\reallyphi$ 7 into a multiple of a 4 $\reallyphi$ 3 series. We also deduce multidimensional extensions of Sears' 4 $\reallyphi$ 3 transformation formula, the second iterate of Heine's transformation, the q -Gauss summation theorem, and of the q -binomial theorem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s003659900089
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