On some weighted sum formulas involving general multiple zeta-type series
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F19%3A10242805" target="_blank" >RIV/61989100:27510/19:10242805 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022314X19301829?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022314X19301829?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2019.05.003" target="_blank" >10.1016/j.jnt.2019.05.003</a>
Alternative languages
Result language
angličtina
Original language name
On some weighted sum formulas involving general multiple zeta-type series
Original language description
The purpose of this paper is a study of the general finite sums Phi N,d(K) := Sigma(N >= n1 >=...>= nk >= 1) Pi(K)(j=1) A (inverted right perpendicular nj/d inverted left perpendicular), d is an element of N, that generalize the truncated multiple harmonic sums zeta(star)(N)({s}(K)) corresponding to d = 1 and A(n) = 1/n(s) with s is an element of N. Surprisingly, when specializing our general transformation result concerning Phi(dN,d)(K), such a type of finite sums can be used for generating and closed-form evaluation of new linear combinations of multiple Hurwitz zeta-star values of the form Sigma(s proves K max(s)<= d) zeta(star) (cs; a). Pi(l(s))(r=1) ((-1)(sr-1).(d s(r))), assuming (a, c, d, K) is an element of R x N-3 with a > -1, c > 1, where the sum is extended over all compositions of K with maximal part not exceeding d. (C) 2019 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Number Theory
ISSN
0022-314X
e-ISSN
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Volume of the periodical
205
Issue of the periodical within the volume
December 2019
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
124-147
UT code for WoS article
000483456600007
EID of the result in the Scopus database
2-s2.0-85067472827