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Explicit evaluation of harmonic sums

Ce Xu
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회논문집 (Communications of the KMS)|제33권 제1호|pp. 13-36

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참고문헌

키워드

Stirling numberRiemann zeta functionharmonic numberEuler sum
주제분류수학

초록

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

Abstract

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

참고문헌 (34)

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