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Generalized Powers of Substitution with Pre-Function Operators

DOI: 10.4236/am.2013.47A004, PP. 12-17

Keywords: Formal Power Series, Formal Substitution, Riordan Group, Generalized Powers, Sheffer Sequences, Umbral Calculus

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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+\"\"(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\"\" .

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