The Abel Lemma and the 𝑞-Gosper Algorithm

Chen, Vincent; Chen, William; Gu, Nancy

doi:10.1090/S0025-5718-07-01968-0

The Abel Lemma and the $q$-Gosper Algorithm
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by Vincent Y. B. Chen, William Y. C. Chen and Nancy S. S. Gu;

Math. Comp. 77 (2008), 1057-1074

DOI: https://doi.org/10.1090/S0025-5718-07-01968-0

Published electronically: October 24, 2007

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Abstract:

Chu has recently shown that the Abel lemma on summation by parts reveals the telescoping nature of Bailey’s ${}_6\psi _6$ bilateral summation formula. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the $q$-Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas.

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