CONNECTION FORMULAS FOR 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH A COMPLEX PARAMETER AND HAVING AN ARBITRARY NUMBER OF TURNING-POINTS

We consider the differential equation () -u'' + chi(x)u = rhop2phi2(x )u on a finite interval I, where I contains m turning points, that is here, zeros of phi. Using asymptotic estimates proved by R. E. LANGER for solutions of () for intervals containing only one turning point w e derive asymptotic estimates (for rho --> infinity) for a special fun damental system of solutions of () in I. The results obtained are fun damental for the investigation of eigenvalue problems defined by () a nd suitable boundary conditions.