Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Raed S. Batahan and A. Shehata
Pages: [47] - [59]
Received Date: May 3, 2014
Submitted by:
The main purpose of this paper is to present Hermite-Chebyshev polynomials and to give some properties of Hermite and Chebyshev polynomials. We derive operational identities, generating functions, and integral representation for power series satisfied by Hermite, Chebyshev, and Hermite-Chebyshev polynomials. Furthermore, for these Hermite-Chebyshev polynomials, we give operational rules with operators, often exploited in the theory of exponential operators. Finally, some definitions of Hermite-Chebyshev polynomials also of two, three and in turn several index are derived and new families of polynomials.
Hermite and Chebyshev polynomials, operational calculus, generating functions, integral transform, exponential operators, multi-index Hermite-Chebyshev polynomials.
