Bernoulli and Euler Polynomials in Clifford Analysis

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• 作者：G.F. Hassan ; L. Aloui
• 关键词：Bernoulli polynomials ; Euler polynomials ; special monogenic polynomials ; Appell polynomials ; umbral calculus
• 刊名：Advances in Applied Clifford Algebras
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：25
• 期：2
• 页码：351-376
• 全文大小：821 KB
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• 作者单位：G.F. Hassan (1) (2)
  L. Aloui (3)
  
  1. Department of Mathematics, Faculty of Science, Northern Borders University, Arar, P.O. Box 1321, Kingdom of Saudi Arabia
  2. Department of Mathematics, Faculty of Science, University of Assiut, P.O. Box 71516, Assiut, Egypt
  3. Department of Mathematics, Faculty of Sciences, Northern Borders University, Arar, P.O. Box 1321, Kingdom of Saudi Arabia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Mathematical Methods in Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-4909

文摘

In this article, we bring a new set of Bernoulli and Euler special monogenic polynomials. It is based on the umbral calculus adapted to the Clifford setting, which is equivalent to a polynomial representation using a special set of Appell polynomials. Also, we study the convergence properties (the effectiveness) for the Bernoulli and Euler polynomials in Clifford analysis. Finally, some results concerning the mode of increase (the order and type) for these sets are obtained.