ABSTRACT
Many applications in physics and engineering involve the solution of linear, second-order differential equations, which fall into a class of problems known as Sturm-Liouville eigenvalue problems. Such problems consist of a linear, second-order, ordinary differential equation containing a parameter whose value is determined so that the solution to the equation satisfies a given boundary condition. Thus, Sturm-Liouville problems are special kinds of boundary value problems for certain types of ordinary differential equations. The set of orthogonal functions generated by the solution to such problems may be used as basis functions for the Fourier expansion method of solving partial differential equations as well as other important problems. The special functions we briefly introduce in this chapter arise from one or another Sturm-Liouville problem and will be discussed in more detail later in the book.
