More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated D...

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers o...

In this paper, we establish a new asymptotic expansion related to the Wallis ratio. By using exponential Bell polynomials, show that coefficients of can be recursively determined. addition, an explicit expression for is given. Our results improve and generalize existing ones [1].

The direct spreading measures of the Laguerre polynomials L (α) n (x), which quantify the distribution of its Rakhmanov probability density ρn,α(x) = 1 dn xαe−x [ L (α) n (x) ]2 along the positive real line in various complementary and qualitatively different ways, are investigated. These measures include the familiar rootmean-square or standard deviation and the information-theoretic lengths o...

This work is based on the Euler-Seidel matrix method [11] which is related to algorithms, combinatorics and generating functions. This method is quite useful to investigate properties of some special numbers and polynomials. In this paper we consider the Euler-Seidel matrix method for some combinatorial numbers and polynomials. This method is relatively easier than the most of combinatorial met...