Semi-finite forms of bilateral basic hypergeometric series

Chen, William; Fu, Amy

doi:10.1090/S0002-9939-05-08173-6

Semi-finite forms of bilateral basic hypergeometric series
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by William Y. C. Chen and Amy M. Fu

Proc. Amer. Math. Soc. 134 (2006), 1719-1725

DOI: https://doi.org/10.1090/S0002-9939-05-08173-6

Published electronically: December 5, 2005

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Abstract:

We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s $_{1}\psi _{1}$ summation, Bailey’s $_{2}\psi _{2}$ transformations, and Bailey’s $_{6}\psi _{6}$ summation.

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