Related papers: Touchard like polynomials and generalized Stirling…
This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{\lambda x})$, where $\lambda\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an…
We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…
We generalise Ehrhard and Regnier's Taylor expansion from pure to probabilistic $\lambda$-terms through notions of probabilistic resource terms and explicit Taylor expansion. We prove that the Taylor expansion is adequate when seen as a way…
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard polynomials and the Poisson distribution. We also introduce a rather novel permutation…
In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing…
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…
We calculate the formal analytic expansions of certain formal translations in a space of formal iterated logarithmic and exponential variables. The results show how the algebraic structure naturally involves the Stirling numbers of the…
We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…
Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that…
Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…