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 s_{μ,ν}(z) and S_{μ,ν}(z), introduced by ,

where J_ν(z) is a Bessel function of the first kind and Y_ν(z) a Bessel function of the second kind.

The s function can also be written as

where _pF_q is a generalized hypergeometric function.

See also

• Anger function
• Lommel polynomial
• Struve function
• Weber function

References

External links

• Weisstein, Eric W. "Lommel Differential Equation." From MathWorld—A Wolfram Web Resource.
• Weisstein, Eric W. "Lommel Function." From MathWorld—A Wolfram Web Resource.