Acta Scientific Applied Physics (ASAP)

Mini Review Volume 2 Issue 7

On Hermite Polynomials and their Generalizations

Clemente Cesarano1* and William Ramírez2

1Universitá Telematica Internazionale Uninettuno, Rome, Italy
2Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia

*Corresponding Author: Clemente Cesarano, Universitá Telematica Internazionale Uninettuno, Rome, Italy.

Received: May 23, 2022; Published: June 29, 2022

Abstract

The article is written with the objective of carrying out a study on Hermite polynomials and their respective generalizations. Additionally, we will show the applications they have in the field of special functions and their relations with Bernoulli polynomials, Euler polynomials, Genocchi polynomials and Frobenius-Euler polynomials.

Keywords: Bernoulli Polynomials; Hermite Polynomials; Genocchi Polynomials and Euler Polynomials

References

  1. Andrews Larry C. “Special functions for Engineers and Applied Mathematicians”. Macmillan USA, (1985).
  2. Appell P and J Kampé de Fériet. “Fonctions Hypergéométriques et Hypersphériques Polynomes d JHermite”. Paris: Gautier Villars (1926).
  3. Cesarano C., et al. “Finite sums and generalized forms of Bernoulli polynomials”. Rendiconti di Mathematica 19 (1999): 385-391.
  4. Dattoli G. “Generalized polynomials operational identities and their applications”. Journal of Computational and Applied Mathematics 118 (2000): 111-123.
  5. Ozarslan MA. “Unified Apostol-Bernoulli, Euler and Genocchi polynomials”. Computers and Mathematics with Applications 62 (2011): 2452-2462.
  6. Srivastava H M and J Choi. “Series associated with the Zeta and related functions”. Springer, Dordrecht, Netherlands (2001).
  7. Serkan A., et al. “A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications”. Symmetry (2018).
  8. Srivastava HM and Choi J. “Zeta and q-Zeta Functions and Associated Series and Integrals”. Elsevier, London (2012).
  9. “A new class of generalized Hermite-Bernoulli polynomials”. Georgian Mathematical Journal 19 (2012): 559-573.

Citation

Citation: Clemente Cesarano and William Ramírez. “On Hermite Polynomials and their Generalizations". Acta Scientific Applied Physics 2.7 (2022): 12-13.

Copyright

Copyright: © 2022 Clemente Cesarano and William Ramírez. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.




Metrics

Acceptance rate32%
Acceptance to publication20-30 days
Impact Factor1.014

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