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CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES

Published online by Cambridge University Press:  02 February 2004

WILLIAM Y. C. CHEN  and
AMY M. FU
WILLIAM Y. C. CHEN
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. [email protected]
AMY M. FU
Affiliation:
Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. [email protected]
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Abstract

The authors present a technique of deriving basic hypergeometric identities from specializations using fewer parameters, by using the classical Cauchy identity on the expansion of the power of $x$ in terms of the $q$-binomial coefficients. This method is referred to as ‘Cauchy augmentation’. Despite its simple appearance, the Cauchy identity plays a key role in parameter augmentation. For example, one can reach the $q$-Gauss summation formula from the Euler identity by using the Cauchy augmentation twice. This idea also applies to Jackson's $_2\phi_1$ to $_3\phi_1$ transformation formula. Moreover, a transformation formula analogous to Jackson's formula is obtained.

Keywords

05A3033D15
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 2 , March 2004 , pp. 169 - 175
Copyright
© The London Mathematical Society 2004

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