On a parametric K-fold series and its connection to Nielsen-Kölbig relations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F23%3A10251948" target="_blank" >RIV/61989100:27510/23:10251948 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022247X22009921" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X22009921</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126978" target="_blank" >10.1016/j.jmaa.2022.126978</a>

Result language
angličtina
Original language name
On a parametric K-fold series and its connection to Nielsen-Kölbig relations
Original language description
The goal of this paper is twofold. First, we investigate the generating function of the parametric sum Sigma(n1 >=...>= nK >= 1) Pi(K)(j=1) 1/n(j) . (n(j) + x), K is an element of N, where x is real with vertical bar x vertical bar < 1. With the help of this approach, we generate a class of multiple zeta-star sums S*(K,lambda) := Sigma zeta*(s) with vertical bar s vertical bar = 2K + lambda, s(i) >= 2, lambda is an element of N-0, and evaluate them as special polynomial values at zeta(i). Second, as a somewhat surprising application, we restate our result concerning S*(K,lambda) with the help of the non-starred alternating multiple zeta values of the form zeta(<(u)over bar>, {1}(v)) and establish a new system of equations connected with Nielsen-Kolbig relations. This enables us a relatively direct insight into the dependence among such specific values. (c) 2022 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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