Lommel Polynomial

The Lommel polynomials  arise from the equation

(1)

where  is a Bessel function of the first kind and  is a complex number (Watson 1966, p. 294). The function is given for  by

			(2)
			(3)

where  is a gamma function,  is a Bessel function of the first kind, and  is a generalized hypergeometric function. Since (1) must reduce to the usual recurrence formula for Bessel functions, it follows that

			(4)
			(5)

REFERENCES:

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1477, 1980.

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, p. 294, 1966.