C
n
and D
n
Very-Well-Poised
10
φ
9
Transformations |
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Authors: | G Bhatnagar M Schlosser |
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Institution: | Department of Mathematics The Ohio State University Columbus OH 43210 USA, US M. Schlosser Institut für Mathematik der Universit?t Wien Strudlhofgasse 4, A-1090 Wien Austria, AUSTRIA
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Abstract: | In this paper we derive multivariable generalizations of Bailey's classical terminating balanced very-well-poised
10
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
9
transformations combined with A
n
, C
n
, and D
n
extensions of Jackson's
8
7
summation. Milne and Newcomb have previously obtained an analogous formula for A
n
series. Special cases of our
10
9
transformations include several new multivariable generalizations of Watson's transformation of an
8
7
into a multiple of a
4
3
series. We also deduce multidimensional extensions of Sears'
4
3
transformation formula, the second iterate of Heine's transformation, the q -Gauss summation theorem, and of the q -binomial theorem.
August 28, 1996. Date revised: September 8, 1997. |
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Keywords: | , Multiple basic hypergeometric series associated to root systems An , Cn , and Dn , Jackson's 8φ,7 summations, Terminating,,,,,10φ,9 transformations, Watson's transformations, Sears' 4φ,3 transformations, Heine's 2φ,1 transformation, q -Gauss summation,,,,,,q -Binomial theorem, AMS Classification, Primary 33D70, Secondary 05A19, 33D20, |
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