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Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values

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  • Yuan He
  • Zhuoyu Chen
  • Li Guo

Abstract

We perform a further investigation for the multiple zeta values and their variations and generalizations in this paper. By making use of the method of the generating functions and some connections between the higher-order trigonometric functions and the Lerch zeta function, we explicitly evaluate some weighted sums of the multiple zeta, Hurwitz zeta, and alternating multiple zeta values in terms of the Bernoulli and Euler polynomials and numbers. It turns out that various known results are deduced as special cases.

Suggested Citation

  • Yuan He & Zhuoyu Chen & Li Guo, 2021. "Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, May.
    • Handle: RePEc:hin:jjmath:6672532
    DOI: 10.1155/2021/6672532
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