The Ramanujan Journal

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

A Hypergeometric Hierarchy for the Andrews Evaluations

  • D. Stanton


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