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We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.
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참고문헌 (7)
참고문헌 신청
W. N. Bailey / 1928 / Product of generalized hypergeometric series / Proc. London Math. Soc 228:242~254
W. N. Bailey / 1964 / Generalized Hypergeometric Series / Stechert Hafner
J. Choi / 2010 / Contiguous extensions of Dixon's theorem on the sum of a 3F2 / J. In-equal. Appl 2010
김용섭 / 2009 / Applications of generalized Kummer's summation theorem for the series _{2}F_{1} / 대한수학회보 46(6):1201~1211
J. L. Lavoie / 1996 / Generalization of Whipple's theorem on the sum of a 3F2 / J. Comput. Appl. Math 72(2):293~300
W. N. Bailey / 1964 / Generalized Hypergeometric Series / Stechert Hafner
J. Choi / 2010 / Contiguous extensions of Dixon's theorem on the sum of a 3F2 / J. In-equal. Appl 2010
김용섭 / 2009 / Applications of generalized Kummer's summation theorem for the series _{2}F_{1} / 대한수학회보 46(6):1201~1211
J. L. Lavoie / 1996 / Generalization of Whipple's theorem on the sum of a 3F2 / J. Comput. Appl. Math 72(2):293~300
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