Asymptotics of Zeros of the Wright Function

Abstract

The paper deals with the asymptotics of zeros of the Wright function

in the case the parameter $\beta$ is a real number. The exact formulae for the order, the type and the indicator function of the entire function $\phi (\rho, \beta ; z)$ are given for $\rho > –1$. 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.