Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

Open access

Abstract

Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • 1. B. M. Levitan Generalized translation operators and some of their applications. Jerusalem: Israel Program for Scientific Translations 1964.

  • 2. Y. Smirnov and A. V. Turbiner Hidden sl 2-algebra of finite-difference equations 1 Modern Physics Letters vol. A10 pp. 1795{1801 1995.

  • 3. W. Miller Lie theory and special functions. Academic Press 1968.

  • 4. P. Appell and J. K. de Feriet Fonctions Hypergeometriques et Hyperspheriques: Polynomes d'Hermite. Paris: Gauthier-Villars 1926.

  • 5. H. W. Gould A. Hopper et al. Operational formulas connected with two generalizations of Hermite polynomials Duke Mathematical Journal vol. 29 no. 1 pp. 51{63 1962.

  • 6. C. Cesarano Operational methods and new identities for Hermite polynomials Mathematical Mod- elling of Natural Phenomena vol. 12 no. 3 pp. 44{50 2017.

  • 7. C. Cesarano C. Fornaro and L. Vazquez A note on a special class of Hermite polynomials Interna- tional Journal of Pure and Applied Mathematics vol. 98 no. 2 pp. 261{273 2015.

  • 8. H. Srivastava and H. Manocha Treatise on generating functions. Ney York: John Wiley & Sons 1984.

  • 9. C. Cesarano G. M. Cennamo and L. Placidi Operational methods for Hermite polynomials with applications WSEAS Transaction on Mathematics vol. 13 pp. 925{931 2014.

  • 10. C. Cesarano C. Fornaro and L. Vazquez Operational results in bi-orthogonal Hermite functions Acta Mathematica Universitatis Comenianae vol. 85 no. 1 pp. 43{68 2016.

  • 11. M. Abramowitz and I. A. Stegun Handbook of mathematical functions: with formulas graphs and mathematical tables vol. 55. Courier Corporation 1965.

  • 12. C. Cesarano Generalized Chebyshev polynomials Hacet. J. Math. Stat vol. 43 no. 5 pp. 731{740 2014.

  • 13. C. Cesarano Integral representations and new generating functions of Chebyshev polynomials Rev. Mat. Complut 2015.

  • 14. C. Cesarano and P. Ricci The Legendre polynomials as a basis for Bessel functions International Journal of Pure and Applied Mathematics vol. 111 no. 1 pp. 129{139 2016.

  • 15. G. Dattoli Hermite-Bessel and Laguerre-Bessel functions: a by-product of the monomiality principle 1999.

  • 16. P. Ricci and I. Tavkhelidze An introduction to operational techniques and special polynomials Jour- nal of mathematical sciences vol. 157 no. 1 pp. 161{189 2009.

  • 17. C. Cesarano Generalization of two-variable Chebyshev and Gegenbauer polynomials International Journal of Applied Mathematics and Statistics vol. 53 no. 1 pp. 1{7 2015.

  • 18. C. Cesarano and C. Fornaro Operational identities on generalized two-variable Chebyshev polyno- mials International Journal of Pure and Applied Mathematics vol. 100 no. 1 pp. 59{74 2015.

Search
Journal information
Impact Factor


CiteScore 2018: 0.95

SCImago Journal Rank (SJR) 2018: 0.324
Source Normalized Impact per Paper (SNIP) 2018: 0.73

Mathematical Citation Quotient (MCQ) 2018: 0.27

Target audience:

researchers in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, and medicine

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 339 339 33
PDF Downloads 193 193 14