Powers and Logarithms

Przeworska-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 -