Skip to main content

Duplicate Form of Gould-Hsu Inversions and Binomial Identities

  • Conference paper
Information Computing and Applications (ICICA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7030))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, G.E., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Bailey, W.N.: Generalized Hypergeometric Series. Cambridge University Press, Cambridge (1935)

    MATH  Google Scholar 

  3. Chu, W.: Inversion techniques and combinatorial identities. Boll. Un. Mat. Ital. B-7, 737–760 (1993)

    MathSciNet  MATH  Google Scholar 

  4. Chu, W.: Inversion techniques and combinatorial identities: Strange evaluations of basic hypergeometric series. Compositio Math. 91, 121–144 (1994)

    MathSciNet  MATH  Google Scholar 

  5. Chu, W., Wei, C.: Lengendre inversions and balanced hypergeometric series identities. Discrete Math. 308, 541–549 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gould, H.W., Hsu, L.C.: Some new inverse series relations. Duke Math. J. 40, 885–891 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ma, X.: An extension of Warnaar’s matrix inversion. Proc. Amer. Math. Soc. 133, 3179–3189 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Riordan, J.: Combinatorial Identities. John Wiley & Sons, Inc., New York (1968)

    MATH  Google Scholar 

  9. Warnaar, S.O.: Summation and transformation formulas for elliptic hypergeometric series. Constr. Approx. 18, 479–502 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wei, C.: Applications of Inversions Techniques in Combnatorial Identities. Dalian University of Technology, Dalian (2006) (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wei, C., Gong, D., Li, J. (2011). Duplicate Form of Gould-Hsu Inversions and Binomial Identities. In: Liu, B., Chai, C. (eds) Information Computing and Applications. ICICA 2011. Lecture Notes in Computer Science, vol 7030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25255-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25255-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25254-9

  • Online ISBN: 978-3-642-25255-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics