Integral representations for the generalized Bedient polynomials and the generalized Cesàro polynomials

Integral representations for the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and the generalized Bessel polynomials

“…Upon setting α = α 1 + 1, β = λ 1 , δ = α 2 + 1, γ = λ 2 , x = z = 1, y = x and w = y in our result (45), we obtain the following integral representations for the generalized Cesàro polynomials (see also [11]):…”

“…Srivastava's polynomials S N n (z) and their variants have been widely considered, in recent years, by numerous other workers on the subject (see, for details, González et al [ 11], and Liu et al [13]; see also [21] and the references cited therein).…”

New Generating Function Relations for the q-Generalized Cesàro Polynomials

“…where 2 1 denotes Gauss's hypergeometric series. Lin et al [2] introduced the generalized Cesàro polynomials as follows:…”

“…It is noted that the special case = 1 of (3) reduces immediately to the Cesàro polynomials defined by (2).…”

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

“…], and Lin et al [6], [9, p. 448 et seq. ], [8] and [7], Liu et al [10] and Srivastava et al [14] and [16]; see also [5]). Here, in our present investigation, we consider the polynomial family defined by where (and throughout this paper) (L s ) abbreviates the array of s parameters…”