6533b821fe1ef96bd127ac07

RESEARCH PRODUCT

Indefinite integrals of products of special functions

John T. Conway

subject

Applied Mathematics010102 general mathematicsMathematical analysisTrigonometric integral010103 numerical & computational mathematicsParabolic cylinder functionGeneralized hypergeometric function01 natural sciencesAddition theoremJacobi elliptic functionsOrder of integration (calculus)Special functionsSlater integrals0101 mathematicsAnalysisMathematics

description

ABSTRACTA method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of the method are presented, which applies directly to functions which obey homogeneous differential equations. However, functions which obey inhomogeneous equations can be incorporated into the products and examples are given of integrals involving products of Bessel functions combined with Lommel, Anger and Weber functions. Many new integrals are derived for a selection of special functions, including Bessel functions, associated Legendre functions, and elliptic integrals. A number of integrals of products of Gauss hypergeometric functions are also presented, which seem to be the first integrals of this type. All results presented have been numerically checked with Mathematica.

yearjournalcountryeditionlanguage
2016-11-25Integral Transforms and Special Functions
https://doi.org/10.1080/10652469.2016.1259619