Elgenfunction Expansions Associated With Second Order Differential Equations

General functions can be expanded in a series of functions that are solutions of second order differential equations. These solutions are considered to be 'eigenfunctions' (characteristic functions), which, individually, may have a particular physical property (the eigenvalue). The most common use of this technique is Fourier series, in which functions are decomposed into waves of various frequencies. Also common is the application in quantum mechanics, in which particular eigenfunctions may have defined energies or momentums. Titchmarsh considers the more general applications to be well-known, and focuses this work particularly on the 'singular' case, and intends his audience to be mathematicians rather than physicists.