Computing the real parabolic cylinder functions U(a,x), V(a,x)

Methods for the computation of real parabolic cylinder functions U(a,x) and V(a,x) and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of the order a and the variable x except for the overflow/underflow limitations. By factoring the dominant exponential factor, scaled functions can be computed without practical overflow/underflow limitations. In an accompanying paper we describe the precise domains for these methods and we present the Fortran 90 codes for the computation of these functions.