CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES

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 2φ1 to 3φ1 transformation formula. Moreover, a transformation formula analogous to Jackson's formula is obtained. 2000 Mathematics Subject Classification 05A30, 33D15.