# Powers and Logarithms

Fractional Calculus and Applied Analysis (2004)

- Volume: 7, Issue: 3, page 283-296
- ISSN: 1311-0454

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topPrzeworska-Rolewicz, Danuta. "Powers and Logarithms." Fractional Calculus and Applied Analysis 7.3 (2004): 283-296. <http://eudml.org/doc/11245>.

@article{Przeworska2004,

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].},

author = {Przeworska-Rolewicz, Danuta},

journal = {Fractional Calculus and Applied Analysis},

keywords = {Algebra with Unit; Leibniz Condition; Logarithmic Mapping; Antilogarithmic Mapping; Power Function; algebra with unit; Leibniz condition; logarithmic mapping; antilogarithmic mapping; power function},

language = {eng},

number = {3},

pages = {283-296},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Powers and Logarithms},

url = {http://eudml.org/doc/11245},

volume = {7},

year = {2004},

}

TY - JOUR

AU - Przeworska-Rolewicz, Danuta

TI - Powers and Logarithms

JO - Fractional Calculus and Applied Analysis

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 7

IS - 3

SP - 283

EP - 296

AB - 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].

LA - eng

KW - Algebra with Unit; Leibniz Condition; Logarithmic Mapping; Antilogarithmic Mapping; Power Function; algebra with unit; Leibniz condition; logarithmic mapping; antilogarithmic mapping; power function

UR - http://eudml.org/doc/11245

ER -

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