Title: Bases of special functions and their domains of convergence /
Authors: Saurer, Josef.
Year: 1993
Subjects: Analytic functions.; Convergence.; Functions, Special.; Eigenfunction expansions.; Mathematical physics
Contents: 1. Foundations of the theory. 1.1. Holomorphic operator functions in Frechet spaces. 1.2. Floquet eigenvalue problems (with a regular singular point). 1.3. Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations. 1.4. Biholomorphic images of functions. 1.5. An expansion theorem -- 2. First order differential systems with a regular singular point. 2.1. Fundamental properties. 2.2. Construction of fundamental systems depending holomorphically on parameters. 2.3. A family of second order differential equations. 2.4. Differential equations and special functions of mathematical physics. 2.4.1. Bessel equation, Bessel function. 2.4.2. Whittaker equation, Whittaker function. 2.4.3. Hypergeometric equation, hypergeometric function. 2.4.4. Generalised spherical function -- 3. Floquet eigenvalue problems for first order differential systems with a regular singular point.