Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments Original Research Article

We present two codes to evaluate Parabolic Cylinder Functions {V(a,x), U(a,x)} for integer and half-integer positive values of a and for nonnegative x. The codes are based on the forward application of the recurrence relation for V(a,x), the backward recurrence for U(a,x), the Wronskian relation between V(a,x) and U(a,x), and the evaluation of a continued fraction for the ratio U(a,x)/U(a−1,x). The accuracy obtained is better than 10−12 for 0 < x <1.0 and better than 10−14 for x > 1. We discuss some applications of the codes.