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Some results on parametric Euler sums

Ce Xu
대한수학회 (The Korean Mathematical Society)|2017.07|대한수학회보 (Bulletin of the KMS)|제54권 제4호|pp. 1255-1280

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참고문헌

키워드

Hurwitz zeta functionRiemann zeta functionharmonic numberEuler sum
주제분류수학

초록

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. \cite{BBD2008}. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

Abstract

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. \cite{BBD2008}. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

참고문헌 (25)

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관련 논문AI추천

Parametric Euler Sums of Harmonic NumbersCe Xu, Junjie Quan, Xiaoxue Wei, Xiyu Wang대한수학회 · 대한수학회보2024 · 제61권 제4호Evaluations of some quadratic Euler sumsCe Xu, Xin Si대한수학회 · 대한수학회보2020 · 제57권 제2호Explicit evaluation of harmonic sumsCe Xu대한수학회 · 대한수학회논문집2018 · 제33권 제1호Shifted harmonic sums of order twoAnthony Sofo대한수학회 · 대한수학회논문집2014 · 제29권 제2호Some evaluations of infinite series involving Dirichlet type parametric harmonic numbersCe Xu, Hongyuan Rui, Xiaobin Yin대한수학회 · 대한수학회보2024 · 제61권 제3호Euler sums of generalized hyperharmonic numbersCe Xu대한수학회 · 대한수학회지2018 · 제55권 제5호

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