Further summation formulae related to generalized harmonic numbers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:335

Article

Zheng, De-Yin

关键词: Riemann Zeta function;    hypergeometric series;    symmetric functions;   

DOI  :  10.1016/j.jmaa.2007.02.002

来源: Elsevier

【 摘 要 】

By employing the univariate series expansion of classical hypergeometric series formulae, Shen [L.-C. Shen, Remarks on some integrals and series involving the Stirling numbers and xi (n), Trans. Amer. Math. Soc. 347 (1995) 1391-1399] and Choi and Srivastava [J. Choi, H.M. Srivastava, Certain classes of infinite series, Monatsh. Math. 127 (1999) 15-25; J. Choi, H.M. Srivastava, Explicit evaluation of Euler and related sums, Ramanujan J. 10 (2005) 51-70] investigated the evaluation of infinite series related to generalized harmonic numbers. More summation formulae have systematically been derived by Chu [W. Chu, Hypergeometric series and the Riemann Zeta function, Acta Arith. 82 (1997) 103-118], who developed fully this approach to the multivariate case. The present paper will explore the hypergeometric series method further and establish numerous summation formulae expressing infinite series related to generalized harmonic numbers in terms of the Riemann Zeta function xi (m) with m = 5, 6, 7, including several known ones as examples. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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