Abstract
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials. As a generalization of this problem, we will consider sums of finite products of Fubini polynomials and represent these in terms of orthogonal polynomials. Here, the involved orthogonal polynomials are Chebyshev polynomials of the first, second, third and fourth kinds, and Hermite, extended Laguerre, Legendre, Gegenbauer, and Jabcobi polynomials. These representations are obtained by explicit computations.
Highlights
Introduction and Preliminariesafter fixing some notations, we will state the necessary basic facts on orthogonal polynomials as minimum as possible
For more details on the fascinating realm of orthogonal polynomials, the readers may refer to some standard books on those subjects, for example [1,2]
In the same way as in this study, some sums of finite products of Chebyshev polynomials of the first, second, third and fourth kinds, and those of Legendre, Laguerre, Lucas and Fibonacci polynomials are expressed in terms of Chebyshev polynomials of all kinds and in terms of Hermite, extended Laguerre, Legendre, Gegenbauer and Jacobi polynomials
Summary
After fixing some notations, we will state the necessary basic facts on orthogonal polynomials as minimum as possible. In the same way as in this study, some sums of finite products of Chebyshev polynomials of the first, second, third and fourth kinds, and those of Legendre, Laguerre, Lucas and Fibonacci polynomials are expressed in terms of Chebyshev polynomials of all kinds (see [4,16,17,18,19]) and in terms of Hermite, extended Laguerre, Legendre, Gegenbauer and Jacobi polynomials (see [20,21,22,23]) Those sums of finite products of all such polynomials can be expressed as linear combinations of Bernoulli polynomials. We let the reader refer to the papers [24,25] and the references therein
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
