Lommel polynomial

A Lommel polynomial Rm,&nu;(z) is a polynomial in 1/z giving the recurrence relation
 * $$\displaystyle J_{m+\nu}(z) = J_\nu(z)R_{m,\nu}(z) - J_{\nu-1}(z)R_{m-1,\nu+1}(z) $$

where J&nu;(z) is a Bessel function of the first kind.

They are given explicitly by
 * $$R_{m,\nu}(z) = \sum_{n=0}^{[m/2]}\frac{(-1)^n(m-n)!\Gamma(\nu+m-n)}{n!(m-2n)!\Gamma(\nu+n)}(z/2)^{2n-m}.$$