Generalized Bernoulli numbers and polynomials in the context of the Clifford analysis
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 127-136.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the generalization of the Bernoulli numbers and polynomials for the case of the hypercomplex variables. Multidimensional analogs of the main properties of classic polynomials are proved.
Keywords: generating functions, Clifford analysis.
Mots-clés : hypercomplex Bernoulli polynomials
@article{JSFU_2018_11_2_a0,
     author = {Sreelatha Chandragiri and Olga A. Shishkina},
     title = {Generalized {Bernoulli} numbers and polynomials in the context of the {Clifford} analysis},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a0/}
}
TY  - JOUR
AU  - Sreelatha Chandragiri
AU  - Olga A. Shishkina
TI  - Generalized Bernoulli numbers and polynomials in the context of the Clifford analysis
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 127
EP  - 136
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a0/
LA  - en
ID  - JSFU_2018_11_2_a0
ER  - 
%0 Journal Article
%A Sreelatha Chandragiri
%A Olga A. Shishkina
%T Generalized Bernoulli numbers and polynomials in the context of the Clifford analysis
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 127-136
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a0/
%G en
%F JSFU_2018_11_2_a0
Sreelatha Chandragiri; Olga A. Shishkina. Generalized Bernoulli numbers and polynomials in the context of the Clifford analysis. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 2, pp. 127-136. http://geodesic.mathdoc.fr/item/JSFU_2018_11_2_a0/

[1] R. Fueter, Functions of a Hyper Complex variable, Lecture Notes. Written and supplemented by E. Bareiss, Fall Semester 1948/49, Univ. Zurich, 1950

[2] R.Delanghe, “On regular-analytic functions with values in a Clifford algebra”, Math. Ann., 185 (1970), 91–111 | DOI | MR

[3] K.Gurlebeck, K.Habetha, W.Sprobig, Holomorphic functions in the plane and $n$-dimensional space, Birkhauser Verlag, Basel, 2008 | MR | Zbl

[4] H.R. Malonek, M.I. Falcao, “On paravector valued homogeneous monogenic polynomials with binomial expansion”, Advances in Applied Clifford Algebras, 22:3 (2012), 789–801 | DOI | MR | Zbl

[5] G. Bretti, P. Natalini, P.E. Ricci, “Generalizations of the Bernoulli and Appell Polynomials”, Abstr. Appl. Anal., 2004, 613–623 | DOI | MR | Zbl

[6] F.Costabile, F.Dell'Accio, M.I.Gualtieri, “A new approach to Bernoulli Polynomials”, Rendiconti di Mathematica, Series VII, 26, Roma, 2006, 1–12 | MR | Zbl

[7] V.Lakshmikantham, D.Trigiante, Theory of Difference equations: Numerical Methods and Applications, M. Dekker, New York, 2002 | MR | Zbl

[8] P.Natalini, A.Bernardini, “A generalization of the Bernoulli Polynomials”, J. Appl. Math., 2003, 155–163 | DOI | MR | Zbl

[9] Z.Zhang, J.Wang, “Bernoulli Matrix and its algebraic properties”, Discrete Appl. Math., 154:11 (2006), 1622–1632 | DOI | MR | Zbl

[10] Y.Simsek, “Twisted (h,q)-Bernoulli numbers and polynomials related to twisted $(h,\,q)$-zeta functions and L-function”, J. Math Anal. Appl., 324:2 (2006), 790–804 | DOI | MR | Zbl

[11] Y.Simsek, V.Kurt, D.Kim, “New approach to the complete sum of products of the twisted $(h,\,q)$-Bernoulli numbers and polynomials”, J. Nonlinear Math. phys., 14:1 (2007), 44–56 | DOI | MR | Zbl

[12] Olga A. Shishkina, “Multidimensional Analog of the Bernoulli Polynomials and its Properties”, J. Sib. Fed. Univ. Math. Phys., 9:3 (2016), 384–392 | DOI

[13] L. Aloui, M.A. Abul-Ez, G.F. Hassan, “Bernoulli special monogenic polynomials with the difference and sum polynomial bases”, Complex Variables and Elliptic Equations, 59:5 (2014), 636–637 | DOI | MR

[14] H.R. Malonek, G. Tomaz, “Bernoulli polynomials and Pascal matrices in the context of Clifford analysis”, Discrete Applied Mathematics, 157 (2009), 838–847 | DOI | MR | Zbl

[15] F.Bracks, R.Delanghe, F.Sommen, Clifford analysis, Pitman, Boston–London–Melbourne, 1982 | MR

[16] H. Malonek, “A new hyper complex structure of the Eucledean space $R^{m+1}$ and the concept of hypercomplex differentiability”, Complex variables, 1990, no. 14, 25–33 | MR | Zbl

[17] H.Malonek, “Power series representation for monogenic functions in $R^{m+1}$ based on a permutational product”, Complex Variables, 1990, no. 15, 181–191 | MR | Zbl

[18] H.R.Malonek, “Selected topics in hypercomplex function theory”, Clifford algebras and potential theory, 7, ed. Sirkka-Liisa Eriksson, University of Joensuu, 2004, 111–150 | MR | Zbl