Abstract
In the present sequel to a recent work by Srivastava et al. (Rocky Mt J Math 49 (in press), 2019), the authors propose to show that the real and imaginary parts of a general set of complex Appell polynomials can be represented in terms of the Chebyshev polynomials of the first and second kind. Furthermore, by applying a general technique based upon the monomiality principle and quasi-monomial sets [see, for details, Ben Cheikh (Appl Math Comput 141:63–76, 2003), Dattoli (in: Cocolicchio, Dattoli, Srivastava (eds), Advanced special functions and applications (Proceedings of the Melfi School on advanced topics in mathematics and physics; Melfi, May 9–12), Aracne Editrice, Rome, 2000) and Steffensen (Acta Math 73:333–366, 1941)], the differential equations satisfied by the Bernoulli, Euler and Genocchi polynomials are derived.
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