A new class of Laguerre-based Apostol type polynomials

Analytical properties of extended Hermite-Bernoulli polynomials

“…denotes the extended Euler polynomials. For λ = 1, these extended Euler polynomials are easily reduces to the generalized Euler polynomials E given in[7]. From (6.1), we conclude that the Hermite-Euler polynomials H E…”

“…On taking α = 1, (1.8) easily reduces to (1.7). For more details about the Bernoulli numbers, Bernoulli polynomials and Hermite-Bernoulli polynomials, we refer to see, for example, [6][7][8] and the references cited therein. The aim of this article is to propose a new family of Hermite-Bernoulli polynomials in a unified and generalized form, which is given in the next section.…”

Connection Problem for Sums of Finite Products of Legendre and Laguerre Polynomials

“…Finally, the reader may want to see [20,21] for some other aspects of Legendre and Laguerre polynomials.…”

Implicit Summation Formula for 2-Variable Laguerre-Based Poly-Genocchi Polynomials

“…n (x, y) by applying the generating function(2.1). Such type of identities have been introduced by several authors (see [11], [12], [13], [15]).…”

“…The generalized Bernoulli, Euler and Genocchi polynomials of (real or complex) order α are usually defined by means of the following generating functions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] G (α) n (x) t n n! , (| t |< π; 1 α = 1).…”