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APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES 2F1

  • Kim, Yong-Sup (Department of Mathematics Education Wonkwang University) ;
  • Rathie, Arjun K. (Department of Mathematics Vedant College of Engineering and Technology)
  • Published : 2009.11.30

Abstract

The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series $_3F_2$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Lavoie, Grondin, and Rathie.

References

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  2. W. N. Bailey, Product of generalized hypergeometric series, Proc. London Math. Soc. Ser. 2 28 (1928), 242-254 https://doi.org/10.1112/plms/s2-28.1.242
  3. B. C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1987
  4. Y. S. Kim and A. K. Rathie, On an extension formulas for the triple hypergeometric series $X_8$ due to Exton, Bull. Korean Math. Soc. 44 (2007), no. 4, 743-751 https://doi.org/10.4134/BKMS.2007.44.4.743
  5. 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 (1996), no. 2, 293-300 https://doi.org/10.1016/0377-0427(95)00279-0
  6. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960
  7. W. N. Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32 Stechert-Hafner, Inc., New York 1964

Cited by

  1. GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN vol.34, pp.1, 2012, https://doi.org/10.5831/HMJ.2012.34.1.35
  2. GENERALIZATION OF A RESULT INVOLVING PRODUCT OF GENERALIZED HYPERGEOMETRIC SERIES DUE TO RAMANUJAN vol.22, 2013, https://doi.org/10.1142/S2010194513010854
  3. ON A NEW CLASS OF SERIES IDENTITIES vol.37, pp.3, 2015, https://doi.org/10.5831/HMJ.2015.37.3.339