On General Alternating Tornheim-Type Double 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 17, 1-30

Abstract: In this paper, we express ∑ n , m ≥ 1 ε 1 n ε 2 m M n ( u ) M m ( v ) n r m s ( n + m ) t as a linear combination of alternating multiple zeta values, where ε i ∈ { 1 , − 1 } and M k ( u ) ∈ { H k ( u ) , H ¯ k ( u ) } , with H k ( u ) and H ¯ k ( u ) being harmonic and alternating harmonic numbers, respectively. These sums include Subbarao and Sitaramachandrarao’s alternating analogues of Tornheim’s double series as a special case. Our method is based on employing two different techniques to evaluate the specific integral associated with a 3-poset Hasse diagram.

Keywords: alternating multiple zeta values; generalized alternating harmonic numbers; Mordell–Tornheim series; alternating Tornheim-type double series; 3-poset integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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