Three-Term Recurrence Relations

Abstract

There are many problems in mathematics and science where a solution function can be represented in terms of special functions. These functions are distinguished by special properties, which make them particularly suitable for the problem under consideration, and which often allow for simple construction. The study and use of special functions is an old branch of mathematics to which many outstanding mathematicians have contributed. Recently this area has experienced a resurgence because of new discoveries and extended computational capabilities (e.g., through symbolic computation). As examples of classical special functions, let us mention here the Chebyshev, Legendre, Jacobi, Laguerre, and Hermite polynomials and the Bessel functions. In the next section, we shall use some of these polynomials and derive the pertinent and important properties.