Abstract
We introduce the concept of a Jackson integral of type BC 1 which is a q-series permitting Weyl group symmetry. Using this, we give a simple proof of transformation formulas for a very-well-poised-balanced 2r ψ 2r hypergeometric series discovered by Sears and Slater.
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This work was supported in part by Grant-in-Aid for Scientific Research (C) No. 17540034 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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Ito, M., Sanada, Y. On the Sears–Slater basic hypergeometric transformations. Ramanujan J 17, 245–257 (2008). https://doi.org/10.1007/s11139-006-9012-6
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DOI: https://doi.org/10.1007/s11139-006-9012-6
Keywords
- Very-well-poised 2r ψ 2r series
- Sears–Slater transformations
- Jackson integral of type BC 1
- Jackson integral of Jordan–Pochhammer type