On Some General Tornheim-Type Series

Kwang-Wu Chen ()
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Kwang-Wu Chen: Department of Mathematics, University of Taipei, Taipei 100234, Taiwan

Mathematics, 2024, vol. 12, issue 12, 1-18

Abstract: In this paper, we solve the open problem posed by Kuba by expressing ∑ j , k ≥ 1 H k ( u ) H j ( v ) H j + k ( w ) j r k s ( j + k ) t as a linear combination of multiple zeta values. These sums include Tornheim’s double series as a special case. Our approach is based on employing two distinct methods to evaluate the specific integral proposed by Yamamoto, which is associated with the two-poset Hasse diagram. We also provide a new evaluation formula for the general Mordell–Tornheim series and some similar types of double and triple series.

Keywords: multiple zeta values; harmonic numbers; Mordell–Tornheim series; Euler sums; Yamamoto’s integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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