TITLE:
Generalized Powers of Substitution with Pre-Function Operators
AUTHORS:
Laurent Poinsot
KEYWORDS:
Formal Power Series; Formal Substitution; Riordan Group; Generalized Powers; Sheffer Sequences; Umbral Calculus
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7A,
July
5,
2013
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 formt+(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 .