JournalszaaVol. 19, No. 2pp. 583–595

Asymptotics of Zeros of the Wright Function

  • Yu. 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=0zkk!Γ(ρk+β)(ρ>1)\phi (\rho, \beta; z) = \sum^{\infty}_{k=0} \frac{z^k}{k! \Gamma (\rho k + \beta)} \\ (\rho > –1)

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

Cite this article

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

DOI 10.4171/ZAA/970