International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 445-458
doi:10.1155/S0161171299224453

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

Abstract

We introduce the notions of Ritt order and type to functions defined by the series ∑n=1∞fn(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.