호남수학학술지 (Honam Mathematical Journal)

  • 제35권1호
  • /
  • Pages.83-92
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  • 2013
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION

  • 투고 : 2013.02.04
  • 심사 : 2013.02.12
  • 발행 : 2013.03.25
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초록

The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of $_3F_2$ and the generalized Kummer's theorem for $_2F_1$ obtained earlier by Lavoie et al. [3, 5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

키워드

참고문헌

  1. W.N Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.
  2. B.C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1985.
  3. J.L. Lavoie, F. Grondin, A.K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a $_3F_2$, Math. Comp. 62(205) (1994), 267-276.
  4. J.L Lavoie, F Grondin, and A.K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72(2) (1996), 293-300. https://doi.org/10.1016/0377-0427(95)00279-0
  5. T.K. Pogany, A.K. Rathie, and U. Pandey, Generalization of a summation due to Ramanujan, Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi XXX(1-2) (2009), 67-73.
  6. A.K. Rathie, S. Malani, R. Mathur, and J. Choi, Certain summations due to Ramanujan and their generalizations, Bull. Korean Math. Soc. 42(3) (2005), 469-475. https://doi.org/10.4134/BKMS.2005.42.3.469
  7. M.R. Spiegel, Mathematical Handbook, Mc Graw-Hill Book Company, New York, 1968.
  8. H.M. Srivastava and J. Choi, Zeta and q-zeta functions and associated series and integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.