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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Quadratic transformation formulas for basic hypergeometric series
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by Mizan Rahman and Arun Verma PDF
Trans. Amer. Math. Soc. 335 (1993), 277-302 Request permission

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 $\S 2.11$ 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
  • © Copyright 1993 American Mathematical Society
  • 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