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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.
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참고문헌 (7)
참고문헌 신청
B. C. Berndt / 1987 / Ramanujan’s Notebooks, Part II / Springer-Verlag
E. D. Rainville / 1960 / Special Functions / The Macmillan Company
G. E. Andrews / 1999 / Special Functions, Encyclopedia of Mathematics and its Applications / Cambridge University Press : 71 ~
J. L. Lavoie / 1996 / Generalizations of Whipple’s theorem on the sum of a 3F2 / J. Comput. Appl. Math 72 (2) : 293 ~ 300
W. N. Bailey / 1928 / Product of generalized hypergeometric series / Proc. London Math. Soc. Ser. 2 28 : 242 ~ 254
E. D. Rainville / 1960 / Special Functions / The Macmillan Company
G. E. Andrews / 1999 / Special Functions, Encyclopedia of Mathematics and its Applications / Cambridge University Press : 71 ~
J. L. Lavoie / 1996 / Generalizations of Whipple’s theorem on the sum of a 3F2 / J. Comput. Appl. Math 72 (2) : 293 ~ 300
W. N. Bailey / 1928 / Product of generalized hypergeometric series / Proc. London Math. Soc. Ser. 2 28 : 242 ~ 254
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