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Duplicate Form of Gould-Hsu Inversions and Binomial Identities

  • Chuanan Wei
  • Dianxuan Gong
  • Jianbo Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7030)

Abstract

It is well known that inversion techniques have an important role in the development of combinatorial identities. In 1973, Gould and Hsu [6] offered a pair of surprising inverse series relations. Then it was utilized by Chu [3, 4] to study systematically hypergeometric series identities. By applying the duplicate form of Gould-Hsu inversions to a terminating 4 F 3 −series identity form Saalscütz’s theorem, we shall establish a family of binomial identities implying numerous interesting hypergeometric series identities.

Keywords

Duplicate form of Gould-Hsu inversions Binomial identity Hypergeometric series identity 

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References

  1. 1.
    Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Bailey, W.N.: Generalized Hypergeometric Series. Cambridge University Press, Cambridge (1935)zbMATHGoogle Scholar
  3. 3.
    Chu, W.: Inversion techniques and combinatorial identities. Boll. Un. Mat. Ital. B-7, 737–760 (1993)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Chu, W.: Inversion techniques and combinatorial identities: Strange evaluations of basic hypergeometric series. Compositio Math. 91, 121–144 (1994)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chu, W., Wei, C.: Lengendre inversions and balanced hypergeometric series identities. Discrete Math. 308, 541–549 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gould, H.W., Hsu, L.C.: Some new inverse series relations. Duke Math. J. 40, 885–891 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ma, X.: An extension of Warnaar’s matrix inversion. Proc. Amer. Math. Soc. 133, 3179–3189 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Riordan, J.: Combinatorial Identities. John Wiley & Sons, Inc., New York (1968)zbMATHGoogle Scholar
  9. 9.
    Warnaar, S.O.: Summation and transformation formulas for elliptic hypergeometric series. Constr. Approx. 18, 479–502 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Wei, C.: Applications of Inversions Techniques in Combnatorial Identities. Dalian University of Technology, Dalian (2006) (in Chinese)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chuanan Wei
    • 1
  • Dianxuan Gong
    • 2
  • Jianbo Li
    • 3
  1. 1.Department of Information TechnologyHainan Medical CollegeHaikouChina
  2. 2.College of SciencesHebei Polytechnic UniversityTangshanChina
  3. 3.Department of StatisticsThe Chinese University of Hong KongHong KongChina

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