The purpose of this paper is to construct a unified generating function involving the families higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using their functional equations, we investigate some properties these Moreover, derive several connected formulas relations including Miller–Lee polynomials, Laguerre Lagrange Hermite–Miller–Lee

In this article, we study the generalized Bernoulli and Euler polynomials, and obtain relationships between them, based upon the technique of matrix representation.

We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are established.

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm functions, Bernoulli and Euler numbers. Mo...

Keywords: Trigonometric functions Hurwitz zeta function Legendre chi function Lerch zeta function Bernoulli polynomials Euler polynomials a b s t r a c t In this sequel to our recent note [D. Cvijović, Values of the derivatives of the cotangent at rational multiples of π, Appl. Math. Lett. it is shown, in a unified manner, by making use of some basic properties of certain special functions, suc...

Recently, Kim’s work in press introduced q-Bernstein polynomials which are different Phillips’ q-Bernstein polynomials introduced in the work by Phillips, 1996; 1997 . The purpose of this paper is to study some properties of several type Kim’s q-Bernstein polynomials to express the p-adic q-integral of these polynomials on Zp associated with Carlitz’s q-Bernoulli numbers and polynomials. Finall...