Abstract
This paper is motivated by the umbral calculus approach to basic hypergeometric series as initiated by Goldman-Rota, Andrews, and Roman, et al. We develop a method of deriving hypergeometric identities by parameter augmentation, which means that a hypergeometric identity with multiple parameters may be derived from its special case obtained by reducing some parameters to zero. Many classical results on basic hypergeometric series easily fall into this framework.
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© 1998 Birkhäuser
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Chen, W.Y.C., Liu, ZG. (1998). Parameter Augmentation for Basic Hypergeometric Series, I. In: Sagan, B.E., Stanley, R.P. (eds) Mathematical Essays in honor of Gian-Carlo Rota. Progress in Mathematics, vol 161. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4108-9_5
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DOI: https://doi.org/10.1007/978-1-4612-4108-9_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8656-1
Online ISBN: 978-1-4612-4108-9
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