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 J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 3, Pages 384–392 (Mi jsfu497)

Multidimensional analog of the Bernoulli polynomials and its properties

Olga A. Shishkina

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: We consider a generalization of the Bernoulli numbers and polynomials to several variables, namely, we define the Bernoulli numbers associated with a rational cone and the corresponding Bernoulli polynomials. Also, we prove some properties of the Bernoulli polynomials.

Keywords: Bernoulli numbers and polynomials, generating functions, Todd operator, rational cone.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Y26.31.0006 This work is supported by the Russian Federation Government grant to conduct research under the guidance of leading scientists at Siberian Federal University (contract 14.Y26.31.0006).

DOI: https://doi.org/10.17516/1997-1397-2016-9-3-384-392

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UDC: 517.55+517.962.26
Accepted: 20.06.2016
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Citation: Olga A. Shishkina, “Multidimensional analog of the Bernoulli polynomials and its properties”, J. Sib. Fed. Univ. Math. Phys., 9:3 (2016), 384–392

Citation in format AMSBIB
\Bibitem{Shi16} \by Olga~A.~Shishkina \paper Multidimensional analog of the Bernoulli polynomials and its properties \jour J. Sib. Fed. Univ. Math. Phys. \yr 2016 \vol 9 \issue 3 \pages 384--392 \mathnet{http://mi.mathnet.ru/jsfu497} \crossref{https://doi.org/10.17516/1997-1397-2016-9-3-384-392} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412010000014} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Sreelatha Chandragiri, Olga A. Shishkina, “Generalized Bernoulli numbers and polynomials in the context of the Clifford analysis”, Zhurn. SFU. Ser. Matem. i fiz., 11:2 (2018), 127–136
2. Evgeny K. Leinartas, Tatiana I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 712–722
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