Skip to main content
Log in

Hypergeometric identities for 10 extended Ramanujan-type series

  • Published:
The Ramanujan Journal Aims and scope Submit manuscript

Abstract

We prove, by the WZ-method, some hypergeometric identities which relate ten extended Ramanujan type series to simpler hypergeometric series. The identities we are going to prove are valid for all the values of a parameter a when they are convergent. Sometimes, even if they do not converge, they are valid if we consider these identities as limits.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adamchik, V.: A certain series associated with Catalan’s constant. Z. Anal. Anwend. (ZAA) 21, 1–10 (2002)

    MathSciNet  Google Scholar 

  2. Amdeberhan, T., Zeilberger, D.: Hypergeometric series acceleration via the WZ method. Electron. J. Comb. 4 (1997)

  3. Berggren, L., Borwein, J., Borwein, P.: Pi: A Source Book. Springer, New York (1997, 2000)

    MATH  Google Scholar 

  4. Borwein, J., Borwein, P.: Pi and the AGM. Wiley, New York (1987)

    MATH  Google Scholar 

  5. Guillera, J.: Some binomial series obtained by the WZ-method. Adv. Appl. Math. 29, 599–603 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Guillera, J.: Generators of some Ramanujan formulas. Ramanujan J. 11(1), 41–48 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Guillera, J.: About a new kind of Ramanujan type series. Exp. Math. 12(4), 507–510 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Petkovs̆ek, M., Wilf, H.S., Zeilberger, D.: A=B. A.K. Peters Ltd. (1996). Appendix A

  9. Ramanujan, S.: Modular equations an approximations to π. Q. J. Math. 45, 350–372 (1914)

    Google Scholar 

  10. Wilf, H.S., Zeilberger, D.: Rational functions certify combinatorial identities. J. Am. Math. Soc. 3 (1990)

  11. Zeilberger, D.: Closed-form (pun intended!). Contemp. Math. 143 (1993)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jesús Guillera.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guillera, J. Hypergeometric identities for 10 extended Ramanujan-type series. Ramanujan J 15, 219–234 (2008). https://doi.org/10.1007/s11139-007-9074-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11139-007-9074-0

Keywords

Mathematics Subject Classification (2000)

Navigation