منابع مشابه
Generalized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to cn is an infinite, lower triangular array determined by the pair (g(t), f(t)) and has the generic element dn,k = [t/cn]g(t)(f(t))/ck, where cn is a fixed sequence of non-zero constants with c0 = 1. We demonstrate that the generalized Riordan arrays have similar properties to those of the class...
متن کاملAsymptotics for generalized Riordan arrays
A Riordan array is an infinite complex matrix (ars) of a certain type (see below for exact definitions). The Riordan array formalism has been much used recently to study combinatorial questions in analysis of algorithms and other areas. Most work has been concerned with “exact” results. In this article we discuss asymptotics of such arrays. We apply general machinery for deriving asymptotics of...
متن کاملGeneralized Stirling Numbers, Exponential Riordan Arrays, and Toda Chain Equations
We study the properties of three families of exponential Riordan arrays related to the Stirling numbers of the first and second kind. We relate these exponential Riordan arrays to the coefficients of families of orthogonal polynomials. We calculate the Hankel transforms of the moments of these orthogonal polynomials. We show that the Jacobi coefficients of two of the matrices studied satisfy ge...
متن کاملGeneralized Stirling numbers, exponential Riordan arrays and orthogonal polynomials
We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of t...
متن کاملGeneralized Narayana Polynomials, Riordan Arrays, and Lattice Paths
We study a family of polynomials in two variables, identifying them as the moments of a two-parameter family of orthogonal polynomials. The coefficient array of these orthogonal polynomials is shown to be an ordinary Riordan array. We express the generating function of the sequence of polynomials under study as a continued fraction, and determine the corresponding Hankel transform. An alternati...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.12.037