On Some Expansions and Integrals Involving the Parabolic Cylinder Functions

In Art. 1 of the present paper certain indefinite integrals involving D_n(z) are evaluated, in Art. 2 the expansion of the product D_g(z) D_m(z) D_n(z) is obtained in series of the functions D_n(z), in Art, 3 the integral ∫D₀(z) D_p(z) D_m(z) D_n(z) dz is evaluated and in Art, 4 an Addition theorem is found.