(p,q)-Growth of an Entire GASHE Function and the Coefficient βn = |an|/Γ(n+μ+1)

Abstract

The main purpose of this paper is to extend the work concerning the measures of growth of an entire function solution of the generalized axially symmetric Helmholtz equation ∂2u/∂x2+∂2u/∂y2+(2μ/y)(∂u/∂y)=0,  μ>0, by studying the general measures of growth ((p,q)-order, lower (p,q)-order, (p,q)-type, and lower (p,q)-type) in terms of coefficients |an|/Γ(n+μ+1) and the ratios of these successive coefficients.