Special Functions
Special Functions A number of special functions have become important in physics because they arise in frequently encountered situations. Identifying a one-dimensional (1-D) integral as one yielding a special function is almost as good as a straight-out evaluation, in part because it prevents the waste of time that otherwise might be spent trying to carry out the integration. But of perhaps more importance, it connects the integral to the full body of knowledge regarding its properties and evaluation. It is not necessary for every physicist to know everything about all known special functions, but it is desirable to have an overview permitting the recognition of special functions which can then be studied in more detail if necessary. It is common for a special function to be defined in terms of an integral over the range for which that integral converges, but to have its definition extended to a larger domain by analytic continuation in the complex plane (cf. Chapter 11 ) or by