On a Certain Polynomial Analogous to Lommel's Polynomial

In a previous paper (1) the author has shown that the parabolic cylinder function D_n(x) satisfies the relation

D_m+n(x)+(-1)^m(n+1)R_n,m-2(x)D_n(x)+(-1)^mR_n-1,m-1(x)D_n+1(x)=0,

where R_n,m(x) is a polynomial analogous to that of Lommel in the Theory of Bessel Functions.