Lommel function

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