Generalized Mneimneh sums and their application to multiple polylogarithms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F25%3A10255997" target="_blank" >RIV/61989100:27510/25:10255997 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.disc.2024.114318" target="_blank" >https://doi.org/10.1016/j.disc.2024.114318</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2024.114318" target="_blank" >10.1016/j.disc.2024.114318</a>

Result language
angličtina
Original language name
Generalized Mneimneh sums and their application to multiple polylogarithms
Original language description
The purpose of this paper is the study of the binomial sum N-ARY SUMMATIONk=1n(nk)DOT OPERATOR Hk(s)(a)DOT OPERATOR pkDOT OPERATOR (1MINUS SIGN p)nMINUS SIGN k, where Hk(s)(a)=N-ARY SUMMATIONi=1kai/is denotes the parameterized analogue of the k-th harmonic number of order s. For a=s=1, these binomial sums were investigated by Mneimneh, who gave a probabilistic interpretation related to hiring problems. We present a generalization of Mneimneh's summation formula and establish several new identities and a connection of these sums with specific multiple polylogarithms, called unit Euler sums, based upon the Toeplitz limit theorem.
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
10100 - Mathematics

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

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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