Lommel function

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Lommel function

The Lommel differential equation, named after Eugen von Lommel, is an inhomogeneous form of the Bessel differential equation:

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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.

The s function can also be written as[1]

where pFq is a generalized hypergeometric function.

See also

References

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