Abstract
In this paper we investigate the series ∑ ∞ k=1 ( 3k k )−1 k −n x k. Obtaining some integral representations of them, we evaluated the sum of them explicitly forn = 0, 1, 2.
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Andrew G E, Askey R and Joy R, Special Functions (Cambridge: Cambridge University Press) (1999)
Apéry R, Irrationalité ς (2) and ς (3),Journess Arithmétiques de Luminiy, Asrérisque 61 (1979)11–13
Batir N, Integral representations of some series involving ( 2k k )−1 k −n and some related series,Appl. Math. Comp. 147 (2004) 645–667
Bernd B C, Ramanujan’s Notebooks, Part 1 (New York: Springer) (1985)
Borwein J M and Bradley D M, Empirically determined Apéry-like formulas for ς (4n+3),Exp. Math. 6(3) (1997) 181–194
Borwein J M, Broadhurst D J and Kamnitzer J, Central binomial sums, multiple Clausen values and zeta values,Exp. Math. 10(1) (2001) 25–34
Borwein J M and Girgensohn R, Evaluations of binomial series,Aequationes Math. 70 (2005) 25–36
Cohen H, Genéralization d’une construction de Apéry,Bull. Soc. Math. France 109 (1981) 269–281
Lehmer D L, Interesting series involving the central binomial coefficient,Am. Math. Monthly 92(7) (1985) 449–457
Lewin L, Polylogarithms and associated functions (New York: Elsevier North-Holland) (1981)
Sherman T, Summation of Glaisher and Apéry-like series, available at http://math.edu.arizona.edu/~ura/001/sherman.travis/series.pdf.s
Zucker I J, On the series ∑ ∞ k=1 ( 2k k )−1 k −n and related sums,J. Number Theory 20(1) (1985) 92–102
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Batir, N. On the series ∑ ∞ k=1 ( 3k k )−1 k −n x k . Proc. Indian Acad. Sci. (Math. Sci.) 115, 371–381 (2005). https://doi.org/10.1007/BF02829799
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DOI: https://doi.org/10.1007/BF02829799