A family of complex Appell polynomial sets

  • H. M. SrivastavaEmail author
  • Paolo Emilio Ricci
  • Pierpaolo Natalini
Original Paper


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.


Appell polynomials Sheffer polynomials Shift operators Boas–Buck polynomial set Complex Appell polynomials Complex Euler polynomials Complex Genocchi polynomials Monomiality principle and quasi-monomial sets Generating functions Differential equations Chebyshev polynomials of the first and second kind Taylor series expansions 

Mathematics Subject Classification

Primary 11B83 33D99 Secondary 26C05 



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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of Medical Research, China Medical University HospitalChina Medical UniversityTaichungTaiwan, ROC
  3. 3.Dipartimento di MatematicaInternational Telematic University UniNettunoRomeItaly
  4. 4.Dipartimento di Matematica e FisicaUniversità degli Studi Roma TreRomeItaly

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