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REMARK ON A SUMMATION FORMULA FOR THE SERIES 4F3(1)

  • Choi, Junesang (Department of Mathematics, Dongguk University) ;
  • Vyas, Yashoverdhan (Department of Mathematics, School of Engineering, Sir Padampat Singhania University) ;
  • Rathie, Arjun K. (Department of Mathematics, School of Physical sciences, Central University of Kerala)
  • 투고 : 2017.08.29
  • 심사 : 2017.09.19
  • 발행 : 2017.09.30

초록

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.

키워드

참고문헌

  1. J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18(4) (2003), 781-789. https://doi.org/10.4134/CKMS.2003.18.4.781
  2. J. Choi, V. Rohira and A. K. Rathie, Note on the extended Watson's summation theorem for the series $_{4}F_{3}(1)$, (2017), submitted.
  3. Y. S. Kim, M. A. Rakha and A. K. Rathie, Extensions of certain classical summation theorems for the series $_{2}F_{1},\;_{3}F_{2}\;and\;_{4}F_{3}$ with applications in Ramanujan's summations, Int. J. Math. Math. Sci. 2010 (2010), Article ID 309503, 26 pages.
  4. J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a $_{3}F_{2}$, Math. Comput. 62 (1994), 267-276.
  5. J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$, J. Comput. Appl. Math. 72 (1996), 293-300. https://doi.org/10.1016/0377-0427(95)00279-0
  6. E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
  7. L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.
  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.