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The aim of this research note is to provide the sums of the series $$\sum_{k=0}^{\infty}(-1)^{k}\left(\begin{array}{lll} \,a-i\\ \,~~k\end{array} \right)\frac{1}{2^{k}(a+k+1)}$$ for $i=0,\pm{1}, \pm{2},\pm{3},\pm{4},\pm{5}$. The results are obtained with the help of generalization of Bailey's summation theorem on the sum of a ${}_{2}F_{1}$ obtained earlier by Lavoie et al.. Several interesting results including those obtained earlier by Srivastava, Vowe and Seiffert, follow special cases of our main findings. The results derived in this research note are simple, interesting, easily established and (potentially) useful.
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참고문헌 (6)
참고문헌 신청
E. D. Rainville / 1960 / Special Functions / The Macmillan Company
E. E. Kummer / 1836 / ¨Uber die hypergeometrische Reihe / J. Reine Angew. Math 15 : 39 ~ 83
H. M. Srivastava / 1988 / Sums of a certain family of series / Elem. Math 43 (2) : 54 ~ 58
J. Choi / 1999 / Sums of certain classes of series / Comm. Korean Math. Soc 14 (3) : 641 ~ 647
J. L. Lavoie / 1996 / Generalizations of Whipple’s theorem on the sum of a 3F2 / J. Comput. Appl. Math 72 (2) : 293 ~ 300
E. E. Kummer / 1836 / ¨Uber die hypergeometrische Reihe / J. Reine Angew. Math 15 : 39 ~ 83
H. M. Srivastava / 1988 / Sums of a certain family of series / Elem. Math 43 (2) : 54 ~ 58
J. Choi / 1999 / Sums of certain classes of series / Comm. Korean Math. Soc 14 (3) : 641 ~ 647
J. L. Lavoie / 1996 / Generalizations of Whipple’s theorem on the sum of a 3F2 / J. Comput. Appl. Math 72 (2) : 293 ~ 300
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