Bernoulli and Euler polynomials in Clifford analysis. (English) Zbl 1320.30087

Hassan, G. F.; Aloui, L.

Adv. Appl. Clifford Algebr. 25, No. 2, 351-376 (2015).

Summary: 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.

MSC:

30G35

Functions of hypercomplex variables and generalized variables

Keywords:

Bernoulli polynomials; Euler polynomials; special monogenic polynomials; Appell polynomials; umbral calculus

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