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12 Parabolic Cylinder FunctionsComputation

§12.20 Approximations

Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions U(a,b,x) and M(a,b,x)13.2(i)) whose regions of validity include intervals with endpoints x= and x=0, respectively. As special cases of these results a Chebyshev-series expansion for U(a,x) valid when λx< follows from (12.7.14), and Chebyshev-series expansions for U(a,x) and V(a,x) valid when 0xλ follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). Here λ denotes an arbitrary positive constant.