Kasana, H. S. The proximate type and its reference to analytic functions. (English) Zbl 0719.30020 Math. Chron. 19, 35-43 (1990). For a function f analytic in the unit disc the order \(\rho\) and lower order \(\lambda\) satisfy \[ \liminf_{r\to 1}\frac{(1- r)M'(r,f)}{M(r,f)\log M(r,f)}\leq \lambda \leq \rho \leq \limsup_{r\to 1}\frac{(1-r)M'(r,f)}{M(r,f)\log M(r,f)}. \] Further, the type T and lower type t satisfy \[ \liminf_{r\to 1}\frac{M'(r,f)(1-r)^{\rho +1}}{M(r,f)}\leq \rho t\leq \rho T\leq \limsup_{r\to 1}\frac{M'(r,f)(1- r)^{\rho +1}}{M(r,f)}. \] When f has regular growth in the sense that all the above inequalities are replaced by equalities it is shown that \(\log (\beta^{-1}M(r,f)/(1-r)^{-\rho})\) is a proximate type of f for a positive number \(\beta\). Reviewer: C.N.Linden (Swansea) MSC: 30D15 Special classes of entire functions of one complex variable and growth estimates Keywords:proximate order; proximate type PDFBibTeX XMLCite \textit{H. S. Kasana}, Math. Chron. 19, 35--43 (1990; Zbl 0719.30020)