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Title: Powers and Logarithms
Authors: Przeworska-Rolewicz, Danuta
Keywords: Algebra with Unit
Leibniz Condition
Logarithmic Mapping
Antilogarithmic Mapping
Power Function
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 7, No 3, (2004), 283p-296p
Abstract: 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].
ISSN: 1311-0454
Appears in Collections:2004

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