6533b7dbfe1ef96bd1271317
RESEARCH PRODUCT
Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method
John T. Conwaysubject
Differential equationApplied Mathematics010102 general mathematicsMathematical analysis010103 numerical & computational mathematics01 natural sciencessymbols.namesakeLinear differential equationSpecial functionsEuler lagrange methodsymbols0101 mathematicsIncomplete gamma functionAnalysisLinear equationBessel functionLommel functionMathematicsdescription
ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear equations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-11-09 | Integral Transforms and Special Functions |