6533b861fe1ef96bd12c56df

RESEARCH PRODUCT

Indefinite integrals of quotients of special functions

John T. Conway

subject

Pure mathematicsApplied Mathematics010102 general mathematicsRecursion (computer science)010103 numerical & computational mathematicsFunction (mathematics)01 natural sciencesLegendre functionsymbols.namesakeAiry functionSpecial functionssymbolsElliptic integral0101 mathematicsAnalysisQuotientBessel functionMathematics

description

ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.

https://doi.org/10.1080/10652469.2018.1428582