In this paper we establish two symmetric identities on sums of products of Euler polynomials.

Abstract : The object of this paper is to give several properties and applications of the multiple p-adic q-L-function of two variables L (r) p,q (s, z, χ). The explicit formulas relating higher order qBernoulli polynomials, which involve sums of products of higher order q-zeta function and higher order Dirichlet q-L-function are given. The value of higher order Dirichlet p-adic q-L-function fo...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

The main purpose of this article is to derive several convolutions for generalized Bernoulli and Euler–Genocchi polynomials order (r,m), Bn(r,m)(x) An(r,m)(x), respectively. These have been introduced recently contain the Bernoulli, Euler Genocchi as special members. Some our results extend M. Merca others concerning numbers polynomials. Probabilistic interpretations presented are also given.

The Laguerre derivative and its iterations have been used to define new sets of special functions, showing the possibility generating a kind parallel universe for mathematical entities this kind. In paper, we introduce Laguerre-type Appell polynomials, in particular, Bernoulli Euler case, examine set hypergeometric Laguerre–Bernoulli polynomials. We show their main properties indicate possible ...

Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making use of the Caputo-fractional derivative, we derive some new interesting identities of these polynomials. It turns out that some known results are derived as special cases.