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The Abel Lemma and the $ q$-Gosper Algorithm


Authors: Vincent Y. B. Chen, William Y. C. Chen and Nancy S. S. Gu
Journal: Math. Comp. 77 (2008), 1057-1074
MSC (2000): Primary 33D15; Secondary 33F10
Published electronically: October 24, 2007
MathSciNet review: 2373192
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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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Additional Information

Vincent Y. B. Chen
Affiliation: Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China
Email: ybchen@mail.nankai.edu.cn

William Y. C. Chen
Affiliation: Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China
Email: chen@nankai.edu.cn

Nancy S. S. Gu
Affiliation: Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China
Email: gu@nankai.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-07-01968-0
Keywords: The Abel lemma, Abel pairs, basic hypergeometric series, the $q$-Gosper algorithm, Gosper pairs
Received by editor(s): July 26, 2006
Received by editor(s) in revised form: August 2, 2006
Published electronically: October 24, 2007
Additional Notes: This work was supported by the 973 Project on Mathematical Mechanization, the Ministry of Education, the Ministry of Science and Technology, and the National Science Foundation of China.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.