Lommel function

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LommelS1.png
LommelS2.png

The Lommel differential equation is an inhomogeneous form of the Bessel differential equation:

Two solutions are given by the Lommel functions sμ,ν(z) and Sμ,ν(z), introduced by Eugen von Lommel (1880),

where Jν(z) is a Bessel function of the first kind, and Yν(z) a Bessel function of the second kind.

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