대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권4호
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  • Pages.1033-1051
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  • 2024
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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PARAMETRIC EULER SUMS OF HARMONIC NUMBERS

  • Junjie Quan (School of Information Science and Technology Xiamen University Tan Kah Kee College) ;
  • Xiyu Wang (School of Mathematics and Statistics Northeast Normal University) ;
  • Xiaoxue Wei (School of Economics and Management Anhui Normal University) ;
  • Ce Xu (School of Mathematics and Statistics Anhui Normal University)
  • 투고 : 2023.10.08
  • 심사 : 2024.02.29
  • 발행 : 2024.07.31
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초록

In this paper, we define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions, linear and quadratic parametric Euler sums. Furthermore, we also give an explicit evaluation of alternating double zeta values ${\zeta}({\bar{2j}};\,2m+1)$ in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.

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과제정보

Xiaoxue Wei is supported by the Natural Science Foundation (Grant No. Anhui Province 2108085QG304). Ce Xu is supported by the National Natural Science Foundation of China (Grant No. 12101008), the Natural Science Foundation of Anhui Province (Grant No. 2108085QA01) and the University Natural Science Research Project of Anhui Province (Grant No. KJ2020A0057).

참고문헌

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