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The Abel Lemma and the  -Gosper Algorithm |
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| Authors: | Vincent Y B Chen William Y C Chen Nancy S S Gu |
| Institution: | Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China ; Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China ; Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, P. R. China |
| Abstract: | Chu has recently shown that the Abel lemma on summation by parts reveals the telescoping nature of Bailey's  bilateral summation formula. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the  -Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas. |
| Keywords: | The Abel lemma Abel pairs basic hypergeometric series the $q$-Gosper algorithm Gosper pairs |
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