Transformation of generalized multiple Riemann zeta type sums with repeated arguments

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F17%3A10237600" target="_blank" >RIV/61989100:27510/17:10237600 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.12.023" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2016.12.023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.12.023" target="_blank" >10.1016/j.jmaa.2016.12.023</a>

Result language
angličtina
Original language name
Transformation of generalized multiple Riemann zeta type sums with repeated arguments
Original language description
The aim of this paper is the study of a transformation dealing with the general K-fold infinite series of the form Sigma(n1 >=...>= nK >= 1) Pi(K)(j=1) a(nj), especially those, where a(n) = R(n) is a rational function satisfying certain simple conditions. These sums represent the direct generalization of the well-known multiple Riemann zeta -star function with repeated arguments zeta*({s}(K)) when a(n) = 1/n(s). Our result reduces Sigma Pi a(nj) to a special kind of one-fold infinite series. We apply the main theorem to the rational function R(n) = 1/((n + a)(s) + b(s)) in case of which the resulting K-fold sum is called the generalized multiple Hurwitz zeta -star function zeta*(a, b; {s}(K)). We construct an effective algorithm enabling the complete evaluation of zeta*(a, b; {2s}(K)) with a is an element of {0, -1/2}, b is an element of R {0}, (K, s) is an element of N-2, by means of a differential operator and present a simple 'Mathematica' code that allows their symbolic calculation. We also provide a new transformation of the ordinary multiple Riemann zeta-star values zeta*({2s}(K)) and zeta*({3}(K)) corresponding to a = b = 0.
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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