Geodesic
Powers and Logarithms
Fractional calculus and applied analysis, Tome 7 (2004) no. 3, pp. 283-296.

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There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers of logarithmic and antilogarithmic mappings or powers of logarithms and antilogarithms (cf. for instance, the survey of Schinzel S[1].
Keywords: Algebra with Unit, Leibniz Condition, Logarithmic Mapping, Antilogarithmic Mapping, Power Function 
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     author = {Przeworska-Rolewicz, Danuta},
     title = {Powers and {Logarithms}},
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Przeworska-Rolewicz, Danuta. Powers and Logarithms. Fractional calculus and applied analysis, Tome 7 (2004) no. 3, pp. 283-296. http://geodesic.mathdoc.fr/item/FCAA_2004_7_3_a1/