The Lommel polynomials R_(m, ν)(z) arise from the equation J_(m + ν)(z) = J_ν(z) R_(m, ν)(z) - J_(ν - 1)(z) R_(m - 1, ν + 1)(z), where J_ν(z) is a Bessel function of the first kind and ν is a complex number. The function is given by R_(m, ν)(z) = (Γ(ν + m))/(Γ(ν)(z/2)^m) _2 F_3(1/2(1 - m), - 1/2 m;ν, - m, 1 - ν - m; - z^2) (Watson 1966, §9.61, p. 297, eqn. 5; Erdelyi et al. 1981, §7.5.2, p. 34, eqn.

Lommel differential equation | Lommel function