The present work is focused on the study of a cotangent sum associated to zeros Estermann zeta function and Riemann function. We use Bell polynomials generating functions approach give arithmetical proof its Dirichlet series different from that given by M. Th. Rassias.

We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality with each observer choosing the same set of two dichotomic observables. We conclude the existence of direct correspondences between (i) the payoff rule and B...

Given an odd prime p, we provide formulas for the Hensel lifts of polynomial roots modulo p, and give an explicit factorization over the ring of formal power series with integer coe cients for certain reducible polynomials whose constant term is of the form pw with w > 1. All of our formulas are given in terms of partial Bell polynomials and rely on the inversion formula of Lagrange.

The aim of the present paper is to introduce new type integral operators which involve Sheffer polynomials. We investigate approximation properties of the our operators with the help of the universal Korovkin-type property and also establish the rate of convergence by using modulus of continuity, second order modulus of smoothness and Petree’s Kfunctional. Moreover, some examples which include ...

In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties these polynomials. We derive explicit implicit summation formulas their symmetric identities by using different analytical means applying generating functions generalized Frobenius-Euler particular, parametric kinds the are introduced algebraic established. addition, illu...

We discuss the generalized Touchard polynomials introduced recently by Dattoli et al. as well as their extension to negative order introduced by the authors with operationial methods. The connection to generalized Stirling and Bell numbers is elucidated and analogs to Burchnall’s identity are derived. A recursion relation for the generalized Touchard polynomials is established and it is shown t...