Some Double q-Series by Telescoping

Chen, Kwang-Wu

doi:10.3390/math11132949

Mathematics

2023

DOI: 10.3390/math11132949

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Some Double q-Series by Telescoping

Kwang-Wu Chen

Abstract: By means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values ζ(s), the Catalan constant G, log(2), π and several other significant mathematical constants.

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2024

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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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Infinite series involving harmonic numbers and reciprocal of binomial coefficients

Chen,

Yang

2024

MATH

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Some Double q-Series by Telescoping

Abstract: By means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values ζ(s), the Catalan constant G, log(2), π and several other significant mathematical constants.

Cited by 1 publication

References 13 publications

Infinite series involving harmonic numbers and reciprocal of binomial coefficients

Infinite series involving harmonic numbers and reciprocal of binomial coefficients

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