There are several functions called ``Lommel functions.'' One type of Lommel function is the solution to the Lommel
Differential Equation with a Plus Sign,

(1) |

(2) |

(3) |

Lommel functions of two variables are related to the Bessel Function of the First Kind and arise in the theory of
diffraction and, in particular, Mie scattering (Watson 1966, p. 537),

(4) | |||

(5) |

**References**

Chandrasekhar, S. *Radiative Transfer.* New York: Dover, p. 369, 1960.

Watson, G. N. *A Treatise on the Theory of Bessel Functions, 2nd ed.* Cambridge, England: Cambridge University Press, 1966.

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1999-05-25