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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 583–595
DOI: 10.4171/ZAA/970

Published online: 2000-06-30

Asymptotics of Zeros of the Wright Function

Yu. Luchko[1]

(1) Freie Universität Berlin, Germany

The paper deals with the asymptotics of zeros of the Wright function $$\phi (\rho, \beta; z) = \sum^{\infty}_{k=0} \frac{z^k}{k! \Gamma (\rho k + \beta)} \\ (\rho > –1)$$ 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.

Keywords: Wright function, indicator function, asymptotics of zeros, entire functions of completely regular growth

Luchko Yu.: Asymptotics of Zeros of the Wright Function. Z. Anal. Anwend. 19 (2000), 583-595. doi: 10.4171/ZAA/970