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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Applications of Andrews’ basic Lauricella transformation
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by D. M. Bressoud PDF
Proc. Amer. Math. Soc. 72 (1978), 89-94 Request permission

Abstract:

We view Andrews’ transformation for the fourth basic Lauricella function as a multiple summation analog of Heine’s fundamental transformation for $_2{\phi _1}$. This leads to multiple summation analogs of several classical q-series identities, and a new proof of a recent partition theorem.
References
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  • D. M. Bressoud, A new family of partition identities, Pacific J. Math. 77 (1978), no. 1, 71–74. MR 506017, DOI 10.2140/pjm.1978.77.71
  • J. A. Daum, The basic analogue of Kummer’s theorem, Bull. Amer. Math. Soc. 48 (1942), 711–713. MR 7079, DOI 10.1090/S0002-9904-1942-07764-0
  • E. Heine, Handbuch der Kugelfunctionen, Vol. I, Reimer, Berlin, 1878. L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 72 (1978), 89-94
  • MSC: Primary 33A30; Secondary 10A45
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0486677-1
  • MathSciNet review: 0486677