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Generalized Powers of Substitution with Pre-Function Operators
University Paris 13, Paris Sorbonne Cité, LIPN, CNRS, Villetaneuse, France
- 1 University Paris 13, Paris Sorbonne Cité, LIPN, CNRS, Villetaneuse, France
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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+ （t 2 ） 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 .
KeywordsFormal Power SeriesFormal SubstitutionRiordan GroupGeneralized PowersSheffer SequencesUmbral Calculus
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