On a Certain Polynomial Analogous to Lommel's Polynomial

In a recent paper*, Dr. S. C. Mitra has shown that the Parabolic cylinder function, D_n (z), satisfies the relation

D_m+n (x) + ( - 1)ⁿ (n + 1) R_{n, m-2}, (x) D_n (x)

+ ( - l )^m = R_n-1,m-1 (x) D_{n +1} (x) = 0, … (1)

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