Derivatives of Stokes multipliers
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.
scientific article; zbMATH DE number 3906884