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Quadratic transformation formulas for basic hypergeometric series


Authors: Mizan Rahman and Arun Verma
Journal: Trans. Amer. Math. Soc. 335 (1993), 277-302
MSC: Primary 33D15
DOI: https://doi.org/10.1090/S0002-9947-1993-1074149-8
MathSciNet review: 1074149
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Abstract: Starting with some of the known transformation formulas for well-poised $ _2{\phi _1}$ and very-well-poised $ _8{\phi _7}$ basic hypergeometric series we obtain $ q$-analogues of $ 36$ quadratic transformation formulas given in $ \S2.11$ of Higher transcendental functions, Vol. 1, edited by Erdélyi et al. We also derive some new quadratic transformation formulas that give rise to identities connecting very-well-poised but unbalanced $ _{10}{\phi _9}$ series in base $ q$ with very-well-poised and balanced $ _{12}{\phi _{11}}$ series in base $ {q^2}$. A Rogers-Ramanujan type identity is also found as a limiting case.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1074149-8
Keywords: Basic hypergeometric series, balanced and very-well-posed series, quadratic transformation formulas, Rogers-Ramanujan identities
Article copyright: © Copyright 1993 American Mathematical Society

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