The Ramanujan Journal

, Volume 2, Issue 4, pp 499–509 | Cite as

A Hypergeometric Hierarchy for the Andrews Evaluations

  • D. Stanton
Article

Abstract

Several 6F5(1) evaluations are given which generalize Andrews' 5F4(1) evaluations. All such evaluations are shown to be equivalent to transformations for a 4F3(z). The methodology allows for higher evaluations, for example an 8F7(1) is given which specializes to over one hundred 5F4(1) results, including all of Andrews'.

hypergeometric series 

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References

  1. 1.
    G.E. Andrews, “Pfaff's method (I): The Mills-Robbins-Rumsey determinant,” to appear in, Discrete Math. Google Scholar
  2. 2.
    G.E. Andrews, “Pfaff's method (III): Comparison with the WZ method,” Elec. J. Comb. 3 (1996), 517–534.Google Scholar
  3. 3.
    G. Andrews and D. Stanton, “Determinants in plane partition enumeration,” to appear in, Eur. J. Comb. Google Scholar
  4. 4.
    S. Ekhad and D. Zeilberger, “Curing the Andrews syndrome,” to appear in, J. Difference Eq. and Applications.Google Scholar
  5. 5.
    G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, 1990.Google Scholar
  6. 6.
    M. Petkovsek and H. Wilf, “A high-tech proof of the Mills-Robbins-Rumsey determinant formula,” Elec. J. Comb. 3 (1996), 499–502.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • D. Stanton
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolis

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