Derivatives of Stokes multipliers
type: Item
instance of: scholarly article
title: Derivatives of Stokes multipliers
zbMATH Open document ID: 0568.34008
author: Mitsuhiko Kohno
published in: Hiroshima Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: An explicit series solution of the ''Euler-type'' system \(tdx/dt=(A_ 0+tA_ 1+...+t^ qA_ q)x,\) is derived in terms of Stokes' multipliers. Here the \(A_ i\) are constant matrices and t is a complex variable. The technique is a variation of the Frobenius method for scalar equation. Recurrence formulae in terms of their derivatives are given for the Stokes' multipliers. This enables asymptotic expansions for large \(| t|\) to be found. The example of the extended Airy equation \(zy^{(n)}-\delta z^ qy=0\) is used to illustrate the procedure.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 3906884
zbMATH Keywords: series solution
zbMATH Keywords: Stokes' multipliers
zbMATH Keywords: Frobenius method
zbMATH Keywords: Recurrence formulae
zbMATH Keywords: Airy equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3906884