Generalization of the Logarithm Function and of the Exponential Function with Arbitrary Base

Details Generalization of the Logarithm Function and of the Exponential Function with Arbitrary Base Generalization of the Logarithm Function and of the Exponential Function with Arbitrary Base

2008-11-03

arxiv.org/abs/0811.0360v1

Mathematics

Classical Analysis and ODEs

4 pages, 3 figures

Scientific paper

The logarithm function and the exponential function are, by nature, base dependent. Thus, in this paper I introduces an arbitrary base in the logarithm and exponential functions, both dependent on $q$, in order to have $\log_a(x;q)$ and $a_q^x$. Some of the properties of these functions had been analyzed. The logarithm function was applied to the entropy which resulted in the $S_q = k[1 - \sum_{i = 1}^Wp_i^{q}]/[1 - e^{1 - q}]$ expression.

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