International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 29764, 6 pages

Iterates of Volterra operators and indeterminate forms

Pablo Braz e Silva1 and Andrés R. R. Papa2,3

1Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, Recife 50740-540, PE, Brazil
2Observatório Nacional, MCT, Rua General José Cristino 77, São Cristovão, Rio de Janeiro 20921-400, RJ, Brazil
3Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro 20550-900, RJ, Brazil

Received 10 February 2005; Revised 6 January 2006; Accepted 22 January 2006

Copyright © 2006 Pablo Braz e Silva and Andrés R. R. Papa. 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.


We state and prove a theorem showing how iterates of the Volterra operator can be used to evaluate indeterminate forms of type 0/0. This general result allows one to recover the Boltzmann-Gibbs entropy as a limit of a wide class of generalized entropies, as considered in an earlier work.