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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Piquette, Jean C.
Copyright Year	1989
Abstract	An earlier article [J. C. Piquette and A. L. Van Buren, SIAM J. Math. Anal., 15 (1984), pp.845855] 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 straightforward 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.
Starting Page	1260
Ending Page	1269
Page Count	10
File Format	PDF
ISSN	00361410
DOI	10.1137/0520083
e-ISSN	10957154
Journal	SIAM Journal on Mathematical Analysis (SJMAAH)
Issue Number	5
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	1989-09-01
Access Restriction	Subscribed
Subject Keyword	antidifferentiation Antidifferentiation integration systems of differential equations special functions
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Mathematics

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