ABSTRACT
The analytic representation of functions or distributions on the real line is usually given by a Cauchy type formula (Chapter 2, Section 4) [Br] but in some cases may also be given by an orthogonal series. This is evident for periodic functions and distributions for which trigonometric series may be used [W15]. For nonperiodic functions the Hermite series can be used, but i t leads to analytic representations that are no longer of the same form [W16]. For functions wi th compact support, series of Legendre polynomials lead to analytic representations involving Legendre functions of the second kind [W17].
