Applications of generalized Kummer's summation theorem for the series _{2}F_{1}
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series _{3}F_{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 _{2}F_{1} obtained earlier by Lavoie, Grondin, and Rathie.
Abstract
The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series _{3}F_{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 _{2}F_{1} obtained earlier by Lavoie, Grondin, and Rathie.
참고문헌 (7)
- G. E. Andrews, "Special Functions, Encyclopedia of Mathematics and its Applications", pp.71~ (1999), Cambridge University Press
- W. N. Bailey, "Product of generalized hypergeometric series", Proc. London Math. Soc. Ser. 2, 28, pp.242~254 (1928)
- W. N. Bailey, "Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics" (1964), Stechert-Hafner, Inc
- B. C. Berndt, "Ramanujan’s Notebooks, Part II" (1987), Springer-Verlag
- 김용섭, "On an extension formulas for the triple hypergeometric series $X_8$ due to Exton", 대한수학회보, 44(4), pp.743~751 (2007), 대한수학회
- J. L. Lavoie, "Generalizations of Whipple’s theorem on the sum of a 3F2", J. Comput. Appl. Math, 72(2), pp.293~300 (1996)
- E. D. Rainville, "Special Functions" (1960), The Macmillan Company