International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 445-458

On the Ritt order and type of a certain class of functions defined by BE-Dirichletian elements

Marcel Berland

4, rue Dupin, Paris 75006, France

Received 2 September 1997

Copyright © 1999 Marcel Berland. 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 introduce the notions of Ritt order and type to functions defined by the series n=1fn(σ+iτ0)exp(sλn),s=σ+iτ,(σ,τ)R×R(*) indexed by τ0 on R, where (λn)1 is a D-sequence and (fn)1 is a sequence of entire functions of bounded index with at most a finite number of zeros. By definition, the series are BE-Dirichletian elements. The notions of order and type of functions, defined by B-Dirichletian elements, are considered in [3, 4]. In this paper, using a technique similar to that used by M. Blambert and M. Berland [6], we prove the same properties of Ritt order and type for these functions.