n-fold Fourier series expansion in root functions of a differential pencil with n-fold multiple characteristic

Abstract

On a finite interval, we consider a parametric differential pencil of the singular irregular type with an n-fold multiple characteristic and with boundary conditions all of which except for the last are posed at the left end of the interval. We solve the problem on the n-fold expansion of n arbitrary functions in series in Keldysh derived chains of eigenfunctions and associated functions (root functions) of the pencil.