Asymptotics of zeros of the wright function

Abstract

The paper deals with the asymptotics of zeros of the Wright function φ(ρ,βz)=∑k=0∞z k/k!(ρk+β) (ρ > -1) in the case the parameter β is a real number. The exact formulae for the order, the type and the indicator function of the entire function φ(ρ,βz) are given for ρ > -1. On the basis of these results and using the obtained distribution of the zeros of the Wright function it is shown to be a function of completely regular growth. © Heldermann Verlag.