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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A generalization of Euler鈥檚 hypergeometric transformation
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by Robert S. Maier PDF
Trans. Amer. Math. Soc. 358 (2006), 39-57 Request permission

Abstract:

Euler鈥檚 transformation formula for the Gauss hypergeometric function ${}_2F_1$ is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but not linearly. Its consequences for hypergeometric summation are explored. It has as a corollary a summation formula of Slater. From this formula new one-term evaluations of ${}_2F_1(-1)$ and ${}_3F_2(1)$ are derived by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of ${}_2F_1(-1)$ with linearly constrained parameters are derived as well.
References
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Additional Information
  • Robert S. Maier
  • Affiliation: Departments of Mathematics and Physics, University of Arizona, Tucson, Arizona 85721
  • MR Author ID: 118320
  • ORCID: 0000-0002-1259-1341
  • Email: rsm@math.arizona.edu
  • Received by editor(s): April 11, 2003
  • Published electronically: August 25, 2005
  • Additional Notes: This work was partially supported by NSF grant PHY-0099484.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 39-57
  • MSC (2000): Primary 33C20; Secondary 33C05, 34Mxx
  • DOI: https://doi.org/10.1090/S0002-9947-05-04045-6
  • MathSciNet review: 2171222