Generalized Powers of Substitution with Pre-Function Operators

Laurent Poinsot

University Paris 13, Paris Sorbonne Cité, LIPN, CNRS, Villetaneuse, France.

DOI: 10.4236/am.2013.47A004                

Abstract

An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form t+（t²） is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ，σ ）  , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .

Keywords

Formal Power Series; Formal Substitution; Riordan Group; Generalized Powers; Sheffer Sequences; Umbral Calculus

Conflicts of Interest

The authors declare no conflicts of interest.

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