文章基本信息

标题：Differential equations for the extended 2D Bernoulli and Euler polynomials
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作者：Banu Yılmaz ; Mehmet Ali Özarslan
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：107
DOI：10.1186/1687-1847-2013-107
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we introduce the extended 2D Bernoulli polynomials by t α ( e t − 1 ) α c x t + y t j = ∑ n = 0 ∞ B n ( α , j ) ( x , y , c ) t n n ! and the extended 2D Euler polynomials by 2 α ( e t + 1 ) α c x t + y t j = ∑ n = 0 ∞ E n ( α , 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 , α = 1 . On the other hand, all the results for the second family are believed to be new, even in the case c = e , α = 1 . Finally, we give some open problems related with the extensions of the above mentioned polynomials. MSC:11B68, 33C05.
关键词：2 D Bernoulli polynomials ; 2 D Euler polynomials ; 2 D Appell Polynomials ; Hermite-Kampé de Fériet (or Gould-Hopper) polynomials ; differential equations ; generalized heat equation