Two inequalities for parabolic cylinder functions
Frank W. J. Olver · Mathematical Proceedings of the Cambridge Philosophical Society · 1961
In this paper upper bounds are established for the principal solution of the differential equation and its derivative, for unrestricted values of the complex variable t and the complex parameter μ. The results may have little interest in their own right, but they are of great value in developing the asymptotic theory of linear second-order differential equations in a domain containing two turning points. Equation (1·1) is the simplest example of a differential equation of this type.