Asymptotics of Zeros of the Wright Function

Yuri Luchko

doi:10.4171/zaa/970

JournalszaaVol. 19, No. 2pp. 583–595

Asymptotics of Zeros of the Wright Function

Yuri Luchko
Freie Universität Berlin, Germany

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Abstract

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

ϕ (ρ, β; z) = k = 0 \sum \infty \frac{z ^{k}}{k ! Γ ( ρ k + 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 $ϕ (ρ, β; z)$ 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.

Cite this article

Yuri Luchko, Asymptotics of Zeros of the Wright Function. Z. Anal. Anwend. 19 (2000), no. 2, pp. 583–595

DOI 10.4171/ZAA/970