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http://hdl.handle.net/11129/3464
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Title: | Differential equations for the extended 2D Bernoulli and Euler polynomials |
Authors: | Özarslan, Mehmet Ali Yılmaz, Banu Eastern Mediterranean University, Faculty of Arts & Sciences, Department of Mathematics |
Keywords: | generalized heat equation, Functional Analysis, 2 D Appell Polynomials, Mathematics, Difference and Functional Equations, Partial Differential Equations, Analysis Ordinary Differential Equations, Hermite-Kampé de Fériet (or Gould-Hopper) polynomials, 2 D Euler polynomials, Mathematics, general, differential equations, EXTENSIONS, Partial, Fixed point theory, Euler angles, Usage |
Issue Date: | 2013 |
Publisher: | Springer International Publishing AG |
Abstract: | In this paper, we introduce the extended 2D Bernoulli polynomials by t(alpha)/(e(t) - 1)(alpha) c(xt+ytj) = Sigma(infinity)(n=0) B-n((alpha,j)) (x,y,c) t(n)/n! and the extended 2D Euler polynomials by 2(alpha)(e(t) + 1)(alpha) c(xt+ytj) = Sigma(infinity)(n=0) E-n((alpha,j)) (x,y,c) t(n)/n!, where c > 1. By using the concepts of the monomiality principle and factorization method, we obtain the differential, integro-differential and partial differential equations for these polynomials. Note that the above mentioned differential equations for the extended 2D Bernoulli polynomials reduce to the results obtained in (Bretti and Ricci in Taiwanese J. Math. 8(3): 415-428, 2004), in the special case c = e, alpha = 1. On the other hand, all the results for the second family are believed to be new, even in the case c = e, alpha = 1. Finally, we give some open problems related with the extensions of the above mentioned polynomials. |
Description: | The file in this item is the publisher version (published version) of the article. |
URI: | http://dx.doi.org/10.1186/1687-1847-2013-107 http://hdl.handle.net/11129/3464 |
ISSN: | 1687-1847, 1687-1839(print) 1687-1847(online) |
Appears in Collections: | MAT – Journal Articles: Publisher & Author Versions (Post-Print Author Versions) – Mathematics
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