Dmitry V. Dolgy

A Note on Eulerian Polynomials

We study Genocchi, Euler, and tangent numbers. From those numbers we derive some identities on Eulerian polynomials in connection with Genocchi and tangent numbers.

Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus

In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of several special polynomials arising from umbral calculus.MSC: 05A10, 05A19.

Some Formulae for the Product of Two Bernoulli and Euler Polynomials

We investigate some formulae for the product of two Bernoulli and Euler polynomials arising from the Euler and Bernoulli basis polynomials.

A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on Z p

The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind. In this paper, we derive a Witt-type formula for the degenerate Bernoulli polynomials which can be represented by the p-adic invariant integral on Z p . In addition, we introduce the λ -Daehee polynomials and give some relations between the degenerate Bernoulli polynomials and the λ -Daehee polynomials.

Some New Identities on the Bernoulli and Euler Numbers

We give some new identities on the Bernoulli and Euler numbers by using the bosonic p-adic integral on Zp and reflection symmetric properties of Bernoulli and Euler polynomials.

Fourier series of higher-order Bernoulli functions and their applications

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.

Some identities of Genocchi polynomials arising from Genocchi basis

In this paper, we give some interesting identities which are derived from the basis of Genocchi. From our methods which are treated in this paper, we can derive some new identities associated with Bernoulli and Euler polynomials.MSC:11B68, 11S80.

On the Higher-Order q-Euler Numbers and Polynomials with Weight α

The main purpose of this paper is to present a systemic study of some families of higher-order q-Euler numbers and polynomials with weight α. In particular, by using the fermionic p-adic q-integral on ℤp, we give a new concept of q-Euler numbers and polynomials with weight α.

Fourier series of sums of products of ordered Bell and poly-Bernoulli functions

In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those functions in terms of Bernoulli functions.

Degenerate poly-Cauchy polynomials

In this paper, we study several properties for the degenerate poly-Cauchy polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.