Search results for "Lommel function"

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Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method

2015

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…

Differential equationApplied Mathematics010102 general mathematicsMathematical analysis010103 numerical & computational mathematics01 natural sciencessymbols.namesakeLinear differential equationSpecial functionsEuler lagrange methodsymbols0101 mathematicsIncomplete gamma functionAnalysisLinear equationBessel functionLommel functionMathematicsIntegral Transforms and Special Functions
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Bounds for Bessel functions

1989

We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.

symbols.namesakeParticle in a spherically symmetric potentialCylindrical harmonicsBessel processGeneral MathematicsMathematical analysisBessel polynomialsStruve functionsymbolsBessel's inequalityBessel functionLommel functionMathematicsRendiconti del Circolo Matematico di Palermo
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