@misc{Maciuk_Arkadiusz_Remarks_2016,
 author={Maciuk, Arkadiusz and Smoluk, Antoni},
 identifier={DOI: 10.15611/me.2016.12.04},
 year={2016},
 rights={Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy},
 publisher={Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu},
 description={Mathematical Economics, 2016, Nr 12 (19), s. 39-52},
 language={eng},
 abstract={The study shows that the functional equation f (f (x)) = ln(1 + x) has a unique result in a semigroup of power series with the intercept equal to 0 and the function composition as an operation. This function is continuous, as per the work of Paulsen [2016]. This solution introduces into statistics the law of the one-and-a-half logarithm. Sometimes the natural growth processes do not yield to the law of the logarithm, and a double logarithm weakens the growth too much. The law of the one-and-a-half logarithm proposed in this study might be the solution},
 title={Remarks about the square equation : functional square root of a logarithm},
 type={artykuł},
 keywords={functional square root, fractional iteration, power series, logarithm, semigroup},
}