In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.

In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we are going to express those sums of finite products as linear combinations of Bernoulli polynomials. Further, by using a method other than Fourier series expansions, we will be able to express those sums in terms of Euler polynomials.

Recently, Catalan-Daehee numbers are studied by several authors. In this paper, we consider the w-Catalan-Daehee polynomials and investigate some properties for those polynomials. In addition, we give explicit expression for the symmetric identities of the w-Catalan-Daehee polynomials which are derived from p-adic invariant integral on Z p .

In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them. As results, we give some expressions, identities and properties about the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials. 2010 Mathematics Subject Classification. 11B73; 11B83; 05A19. Key words and phrases. extended degenerate Stirling numbers of the second kind, extended degenerate Bell polynomials.

This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations, each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, which involve the hypergeometric functions 1 F 1 and 2 F 1 .