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Semi-finite forms of bilateral basic hypergeometric series |
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| Authors: | William Y C Chen Amy M Fu |
| Institution: | Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People's Republic of China ; Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People's Republic of China |
| 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  summation, Bailey's  transformations, and Bailey's  summation. |
| Keywords: | Bilateral hypergeometric summation semi-finite forms Ramanujan's ${}_{1}\psi _{1}$ summation Bailey's ${}_{2}\psi _{2}$ transformations Bailey's ${}_{6}\psi _{6}$ summation |
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