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 and Sμ,ν, introduced by,
where Jν is a Bessel function of the first kind and Yν a Bessel function of the second kind.
The s function can also be written as
where pFq is a generalized hypergeometric function.