Kasana, H. S.; Sahai, A. The proximate order of entire Dirichlet series. (English) Zbl 0602.30032 Complex Variables, Theory Appl. 9, No. 1-3, 42-62 (1987). The notion of proximate order for an entire Dirichlet series with index- pair (p,q) is introduced and its existence theorem is proved by an elementary technique. The (p,q)-proximate order for a class of entire Dirichlet series is constructed under certain conditions. Also, the lower (p,q)-proximate order is defined and its existence theorem is stated. The authors remark that there exist two proximate orders of a given entire Dirichlet series with index-pair (p,q) and present conditions under which both comparison functions coincide. In the last section, the possibility of proximating a generalized proximate order by some other proximate order is searched. Cited in 1 Document MSC: 30D15 Special classes of entire functions of one complex variable and growth estimates 30B50 Dirichlet series, exponential series and other series in one complex variable Keywords:proximate order; Dirichlet series; index-pair; (p,q)-orders; (p,q)-types; regular (p,q)-growth PDFBibTeX XMLCite \textit{H. S. Kasana} and \textit{A. Sahai}, Complex Variables, Theory Appl. 9, No. 1--3, 42--62 (1987; Zbl 0602.30032) Full Text: DOI