Advertisement

Summable Sums of Hypergeometric Series

  • D. Stanton
Chapter
  • 1.2k Downloads
Part of the Developments in Mathematics book series (DEVM, volume 13)

Abstract

New expansions for certain 2Fl's as a sum of r higher order hypergeometric series are given. When specialized to the binomial theorem, these r hypergeometric series sum. The results represent cubic and higher order transformations, and only Vandermonde's theorem is necessary for the elementary proof. Some q-analogues are also given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gasper, G. and Rahman, M. (1990a). Basic Hypergeometric Series. Cambridge University Press, Cambridge.Google Scholar
  2. Gasper, G. and Rahman, M. (1990b). An indefinite bibasic summation formula and some quadratic, cubic and quartic sums. Canad. J. Math., 42:1–27.MathSciNetGoogle Scholar
  3. Gessel, I. and Stanton, D. (1982). Strange evaluations of hypergeometric series. SIAM J. Math. Anal., 13:295–308.CrossRefMathSciNetGoogle Scholar
  4. Prellberg, T. and Stanton, D. (2003). Proof of a monotonicity conjecture. J. Comb. Th. A, 103:377–381.CrossRefMathSciNetGoogle Scholar
  5. Rahman, M. (1989). Some cubic summation formulas for basic hypergeometric series. Utilitas Math., 36:161–172.zbMATHMathSciNetGoogle Scholar
  6. Rahman, M. (1993). Some quadratic and cubic summation formulas for basic hypergeometric series. Canad. J. Math., 45:394–411.zbMATHMathSciNetGoogle Scholar
  7. Rahman, M. (1997). Some cubic summation and transformation formulas. Ramanujan J., 1:299–308.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. Stanton
    • 1
  1. 1.School of MathematicsMinneapolis

Personalised recommendations