Asymptotic representation of the solutions of a class of systems of linear differential equations
The system (1) \(\sum^{n}_{i=0}A_ i(z)d^{n-i}w/dz^{n-i}=0\) with irregular singular point \(z=\infty\) \((z=0)\) is considered. Here \(w(z)=colon(w_ 1(z),...,w_ q(z)),\) \(A_ i(z)-q\times q\) matrix functions holomorphic in a neighbourhood of \(z=\infty\) \((z=0)\) or having certain other properties. Certain classes of (1) with solutions expressible in the form of asymptotic series of fractional powers of independent variable are investigated. There are close connections with the group of papes mostly from the author.
scientific article; zbMATH DE number 4086072