A Weighted Sum Formula for Alternating Multiple Zeta-Star Values

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F21%3A10248032" target="_blank" >RIV/61989100:27510/21:10248032 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00009-021-01844-z" target="_blank" >https://link.springer.com/article/10.1007%2Fs00009-021-01844-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00009-021-01844-z" target="_blank" >10.1007/s00009-021-01844-z</a>

Result language
angličtina
Original language name
A Weighted Sum Formula for Alternating Multiple Zeta-Star Values
Original language description
In the last decade, many authors essentially contributed to the attractive theory of multiple zeta values. Nevertheless, since their introduction in 1992, there are still many hypotheses and open problems waiting to be solved. The aim of this paper is to develop a method for transforming the multiple zeta-star values. zeta*({2}(K), c) leading to a new sum formula for alternating multiple zeta-star values. Its most simple case has the intelligible form Sigma(c-2)(t=0) (-2)(t+1) Sigma(i >= 2,s is an element of Nt)(i+vertical bar s vertical bar-c) zeta*((i) over bar, s) = (-1)(c) . zeta(c). As a by-product, we also establish a closed form for a new harmonic-like finite summation containing binomial coefficients.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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