충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제36권3호
  • /
  • Pages.149-153
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  • 2023
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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A NOTE ON THE DERIVATIONS OF TWO KNOWN COMBINATORIAL IDENTITIES VIA A HYPERGEOMETRIC SERIES APPROACH

  • Arjun Kumar Rathie (Department of Mathematics Vedant College of Engineering & Technology, (Rajasthan Technical University)) ;
  • Dongkyu Lim (Department of Mathematics Education Andong National University)
  • 투고 : 2023.06.09
  • 심사 : 2023.08.29
  • 발행 : 2023.08.31
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초록

The aim of this note is to derive two known combinatorial identities via a hypergeometric series approach using Saalschiitz's classical summation theorem.

키워드

과제정보

This work was supported by a Research Grant of Andong National University.

참고문헌

  1. G. E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, Cambridge, 2000.
  2. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935; Reprinted by Stechert-Hafner, New York, 1964.
  3. H. W. Gould, Combinatorial Identities, Morgantown Printing and Binding Co., Morgantown, WV. 1972.
  4. Y. S. Kim, M. A. Rakha and A. K. Rathie, Extensions of Certain Classical Summation Theorems for the Series 2F1, 3F2, and 4F3 with Applications in Ramanujan's Summations, Int. J. Math. Sci., 2010 (2010), Article ID 309503, 26 pages.
  5. F. Qi, C.-P. Chen and D. Lim, Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function, Results in Nonlinear Analysis, 4 (2021), no. 1, 57-64. https://doi.org/10.53006/rna.867047
  6. E.D. Rainville, Special Functions, The Macmillan Company, New York. 1960; Reprinted by chelsea Publishing Company, Bronx, NY, 1971.
  7. M. A. Rakha and A. K. Rathie, Generalizations of classical summation theorems for the series 2F1 and 3F2 with applications, Integral Transforms Spec. Funct., 22 (2011), no. 11, 823-840. https://doi.org/10.1080/10652469.2010.549487
  8. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1960.
  9. R. Sprugnoli, Riordan Array Proofs of Identities in Gould's Book, University of Florence, Italy, 2008.