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12 Parabolic Cylinder FunctionsComputation

§12.19 Tables

  • Abramowitz and Stegun (1964, Chapter 19) includes U(a,x) and V(a,x) for ±a=0(.1)1(.5)5, x=0(.1)5, 5S; W(a,±x) for ±a=0(.1)1(1)5, x=0(.1)5, 4-5D or 4-5S.

  • Miller (1955) includes W(a,x), W(a,-x), and reduced derivatives for a=-10(1)10, x=0(.1)10, 8D or 8S. Modulus and phase functions, and also other auxiliary functions are tabulated.

  • Fox (1960) includes modulus and phase functions for W(a,x) and W(a,-x), and several auxiliary functions for x-1=0(.005)0.1, a=-10(1)10, 8S.

  • Kireyeva and Karpov (1961) includes Dp(x(1+i)) for ±x=0(.1)5, p=0(.1)2, and ±x=5(.01)10, p=0(.5)2, 7D.

  • Karpov and Čistova (1964) includes Dp(x) for p=-2(.1)0, ±x=0(.01)5; p=-2(.05)0, ±x=5(.01)10, 6D.

  • Karpov and Čistova (1968) includes e-14x2Dp(-x) and e-14x2Dp(ix) for x=0(.01)5 and x-1 = 0(.001 or .0001)5, p=-1(.1)1, 7D or 8S.

  • Murzewski and Sowa (1972) includes D-n(x) (=U(n-12,x)) for n=1(1)20, x=0(.05)3, 7S.

  • Zhang and Jin (1996, pp. 455–473) includes U(±n-12,x), V(±n-12,x), U(±ν-12,x), V(±ν-12,x), and derivatives, ν=n+12, n=0(1)10(10)30, x=0.5,1,5,10,30,50, 8S; W(a,±x), W(-a,±x), and derivatives, a=h(1)5+h, x=0.5,1 and a=h(1)5+h, x=5, h=0,0.5, 8S. Also, first zeros of U(a,x), V(a,x), and of derivatives, a=-6(.5)-1, 6D; first three zeros of W(a,-x) and of derivative, a=0(.5)4, 6D; first three zeros of W(-a,±x) and of derivative, a=0.5(.5)5.5, 6D; real and imaginary parts of U(a,z), a=-1.5(1)1.5, z=x+iy, x=0.5,1,5,10, y=0(.5)10, 8S.

For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).