We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.

In this paper we derive a general combinatorial identity in terms of polynomials with dual sequences of coefficients. Moreover, combinatorial identities involving Bernoulli and Euler polynomials are deduced. Also, various other known identities are obtained as particular cases.

This paper features the modeling and design of a Robust Decentralized Fast Output Sampling (RDFOS) Feedback control technique for the active vibration control of a smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Eul...

This paper presents a simple approach to invert the matrix P n + I n by applying the Euler polynomials and Bernoulli numbers, where P n is the Pascal matrix.

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.

In this paper we establish some symmetric identities on a sequence of polynomials in an elementary way, and some known identities involving Bernoulli and Euler numbers and polynomials are obtained as particular cases.

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for q-Genocchi numbers and also get the Kummer...

The main purpose of this paper is to derive various Matiyasevich-Miki-Gessel type convolution identities for Bernoulli and Genocchi polynomials and numbers by applying some Euler type identities with two parameters.

The Bernoulli polynomials Bk restricted to 0, 1 and extended by periodicity have nth sine and cosine Fourier coefficients of the formCk/n . In general, the Fourier coefficients of any polynomial restricted to 0, 1 are linear combinations of terms of the form 1/n . If we can make this linear combination explicit for a specific family of polynomials, then by uniqueness of Fourier series, we get a...

Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.