Mathematics > Classical Analysis and ODEs
[Submitted on 22 Mar 2014]
Title:Asymptotics of the Wright function ${}_1Ψ_1(z)$ on the Stokes lines
View PDFAbstract:We investigate a particular aspect of the asymptotic expansion of the Wright function ${}_1\Psi_1(z)$ for large $|z|$. The form of the exponentially small expansion associated with this function on certain rays in the $z$-plane (known as Stokes lines) is discussed. The main thrust of the paper is concerned with the expansion in the particular case when the Stokes line coincides with the negative real axis $\arg\,z=\pi$. Some numerical examples which confirm the accuracy of the expansion are given.
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