Applications of a Technique for Evaluating Indefinite Integrals Containing Products of the Special Functions of Physics.

摘要

An earlier article described an analytical technique for evaluating indefinite integrals involving special functions. The technique replaces the integral by an inhomogeneous set of coupled first-order differential equations. This coupled set does not explicitly contain the special functions of the integrand, and any particular solution of the set is sufficient to obtain an analytical result for the indefinite integral. One difficulty with the technique is that the process of uncoupling one of the functions of the set from the remainder is not straight forward and, in some instances, may be intractable. In the present article, the relevant set is uncoupled for a number of special cases in which the integrand contains one or more Bessel functions, Legendre functions, Hermite functions, or Laguerre functions. The utility of the given analytical expressions is demonstrated by presenting several examples. Several of the indefinite integrals evaluated have not been previously tabulated. Keywords: Special functions; Bessel functions; Integration; Legendre functions; Differential equations; Reprints. (JHD)