Sum Relations from Shuffle Products of Alternating Multiple Zeta Values

Chen, Kwang-Wu

doi:10.1007/s00009-022-02143-x

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…We use the map W, which is defined in Equation ( 6), to transform this two-poset as (xy a 1 ¡ xy a 2 ¡ xy a n )y s+1 . Since (see [23], Equation (4.6))…”

Section: Explicit Formula For Mordell-tornheim Seriesmentioning

confidence: 99%

On Some General Tornheim-Type Series

Chen

2024

Mathematics

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In this paper, we solve the open problem posed by Kuba by expressing ∑j,k≥1Hk(u)Hj(v)Hj+k(w)jrks(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.

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“…We use the map W, which is defined in Equation ( 6), to transform this two-poset as (xy a 1 ¡ xy a 2 ¡ xy a n )y s+1 . Since (see [23], Equation (4.6))…”

Section: Explicit Formula For Mordell-tornheim Seriesmentioning

confidence: 99%

On Some General Tornheim-Type Series

Chen

2024

Mathematics

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On General Alternating Tornheim-Type Double Series

Chen

2024

Mathematics

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In this paper, we express ∑n,m≥1ε1nε2mMn(u)Mm(v)nrms(n+m)t as a linear combination of alternating multiple zeta values, where εi∈{1,−1} and Mk(u)∈{Hk(u),H¯k(u)}, with Hk(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.

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Infinite series involving harmonic numbers and reciprocal of binomial coefficients

Chen,

Yang

2024

MATH

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<abstract>Yamamoto's integral was the integral associated with 2-posets, which was first introduced by Yamamoto. In this paper, we obtained the values of infinite series involving harmonic numbers and reciprocal of binomial coefficients by using some techniques of Yamamoto's integral. We determine the value of infinite series of the form: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \sum\limits_{m_1,\ldots,m_n,\ell_1,\ldots,\ell_k\geq 1}\frac{H_{m_1}^{(a_1)}\cdots H_{m_n}^{(a_n)}} {m_1^{b_1}\cdots m_n^{b_n}\ell_1^{c_1}\cdots\ell_k^{c_k} \binom{m_1+\cdots+m_n+\ell_1+\cdots+\ell_k}{\ell_k}}, $\end{document} </tex-math></disp-formula> in terms of a finite sum of multiple zeta values, for positive integers $ a_1, \ldots, a_n, b_1, \ldots, b_n, c_1, \ldots, c_k $.</abstract>

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Sum Relations from Shuffle Products of Alternating Multiple Zeta Values

Cited by 3 publications

References 16 publications

On Some General Tornheim-Type Series

On Some General Tornheim-Type Series

On General Alternating Tornheim-Type Double Series

Infinite series involving harmonic numbers and reciprocal of binomial coefficients

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