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A family of complex Appell polynomial sets

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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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References

  1. Ben Cheikh, Y.: Some results on quasi-monomiality. Appl. Math. Comput. 141, 63–76 (2003)

    MathSciNet  MATH  Google Scholar 

  2. Boas, R.P., Buck, R.C.: Polynomials defined by generating relations. Am. Math. Mon. 63, 626–632 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boas, R.P., Buck, R.C.: Polynomial Expansions of Analytic Functions. Springer, Berlin (1958)

    Book  MATH  Google Scholar 

  4. Brenke, W.C.: On generating functions of polynomial systems. Am. Math. Mon. 52, 297–301 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bretti, G., Natalini, P., Ricci, P.E.: New sets of Euler-type polynomials. J. Anal. Number Theory 6(2), 51–54 (2018)

    Article  Google Scholar 

  6. Dattoli, G.: Hermite–Bessel and Laguerre–Bessel functions: a by-product of the monomiality principle. In: Cocolicchio, D., Dattoli, G., Srivastava, H.M. (eds) Advanced Special Functions and Applications (Proceedings of the Melfi School on Advanced Topics in Mathematics and Physics; Melfi, May 9–12, 1999), pp. 147–164. Aracne Editrice, Rome (2000)

  7. Dattoli, G., Ricci, P. E., Srivastava, H. M. (Editors).: Advanced Special Functions and Related Topics in Probability and in Differential Equations, Proceedings of the Melfi School on Advanced Topics in Mathematics and Physics (Melfi; June 24–29, 2001), Appl. Math. Comput. 141(1), 1–230 (2003)

  8. Lu, D.-Q., Srivastava, H.M.: Some series identities involving the generalized Apostol type and related polynomials. Comput. Math. Appl. 62, 3591–3602 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo, Q.-M., Srivastava, H.M.: Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials. J. Math. Anal. Appl. 308, 290–302 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Luo, Q.-M., Srivastava, H.M.: Some relationships between the Apostol–Bernoulli and Apostol–Euler polynomials. Comput. Math. Appl. 51, 631–642 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Luo, Q.-M., Srivastava, H.M.: Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind. Appl. Math. Comput. 217, 5702–5728 (2011)

    MathSciNet  MATH  Google Scholar 

  12. Masjed-Jamei, M., Koepf, W.: Symbolic computation of some power-trigonometric series. J. Symbol. Comput. 80, 273–284 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ricci, P.E., Bretti, G., Natalini, P.: New sets of Hahn-type polynomials. J. Anal. (2018) (submitted)

  14. Roman, S.M.: The Umbral Calculus. Academic Press, New York (1984)

    MATH  Google Scholar 

  15. Sheffer, I.M.: Some properties of polynomials sets of zero type. Duke Math. J. 5, 590–622 (1939)

    Article  MathSciNet  MATH  Google Scholar 

  16. Srivastava, H.M., Manocha, H.L.: A Treatise on Generating Functions. Halsted Press (Ellis Horwood Limited), Chichester (1984)

    MATH  Google Scholar 

  17. Srivastava, H.M., Masjed-Jamei, M., Beyki, M.R.: Some new generalizations and applications of the Apostol–Bernoulli, Apostol–Euler and Apostol–Genocchi polynomials. Rocky Mt. J. Math. 49 (in press) (2019)

  18. Steffensen, J.F.: The poweroid, an extension of the mathematical notion of power. Acta Math. 73, 333–366 (1941)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, ROC

    H. M. Srivastava

  3. Dipartimento di Matematica, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, 00186, Rome, Italy

    Paolo Emilio Ricci

  4. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, 1 Largo San Leonardo Murialdo, 00146, Rome, Italy

    Pierpaolo Natalini

Authors
  1. H. M. Srivastava
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  2. Paolo Emilio Ricci
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  3. Pierpaolo Natalini
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Correspondence to H. M. Srivastava.

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Srivastava, H.M., Ricci, P.E. & Natalini, P. A family of complex Appell polynomial sets. RACSAM 113, 2359–2371 (2019). https://doi.org/10.1007/s13398-018-00622-z

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  • DOI: https://doi.org/10.1007/s13398-018-00622-z

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