Laguerre-type Bell polynomials

Integer Sequences Connected with Extensions of the Bell Polynomials

The Encyclopedia of Integer Sequences includes some sequences that are connected with the Bell numbers and that have a particular combinatorial meaning. In this article, we find a general meaning for framing sequences, including the above mentioned ones. Furthermore, by using Laguerre-type derivatives, we derive the Laguerre-type Bell numbers of higher order, showing, as a by-product, that it i...

Laguerre polynomials and Perron-Frobenius operators

Integral Operators Containing Sheffer Polynomials (communicated by Vijay Gupta)

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 ...

Application of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

Direct spreading measures of Laguerre polynomials

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...