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International Journal of Analysis
Volume 2014 (2014), Article ID 195329, 7 pages
http://dx.doi.org/10.1155/2014/195329
Research Article

Some Remarks on the Self-Exponential Function: Minimum Value, Inverse Function, and Indefinite Integral

Departamento de Ciencias Experimentales y Matemáticas, Universidad Católica de Valencia “San Vicente Mártir”, C/Guillem de Castro 96, 46001 Valencia, Spain

Received 9 September 2014; Accepted 10 November 2014; Published 23 November 2014

Academic Editor: Shamsul Qamar

Copyright © 2014 J. L. González-Santander and G. Martín. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Considering the function as a real function of real variable, what is its minimum value? Surprisingly, the minimum value is reached for a negative value of . Furthermore, considering the function , and , two different expressions in closed form for the inverse function can be obtained. Also, two different series expansions for the indefinite integral of and are derived. The latter does not seem to be found in the literature.