The Weber-Fechner law

Author:

Keiichi TAKAHASHI, Go HIRANO, Tetsuya HASEGAWA, Shigeru KANEMITSU, Takayasu KAIDA, Haruo TSUKADA

2010 Mathematics Subject Classication:

91E99, 39B12

Keywords:

functional equation, Gauss' second formula, general distribution property, Hurwitz zeta-function, Lipschitz-Lerch transcendent, Milnor's gamma function, polylogarithm function

Abstract:

In this note, we shall elucidate the reason why the degree of disturbance by noise is measured in logarithmic scale by the Weber-Fechner law in psychometrica. This in turn relies on the solution to the Schröder equation in the theory of functional equations. We shall solve it by the method of [3].

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Taka-et-all-2011

Vol. 6 (14), 2011