Some functional relations for two point boundary value problems—II. the inhomogeneous case

摘要

A set of functional relations analogous to the addition formulas for the trigonometric functions is developed for a class of inhomogeneous linear two point boundary value problems. The relations are implicit ones connecting values of the solutions at three points. For boundary conditions which contain those that appear in scattering and optimal filtering problems, the relations are explicitly solved. The results are expressed in terms of Redheffer's * product, and thus a connection is established with his work on transmission lines and Reid's on the matrix Riccati equation. A numerical algorithm useful for the solution of problems with critical lengths is a principal consequence of these results.