An operator on formal power series of the form SμS , 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 .

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