12 Parabolic Cylinder Functions Computation 12.18 Methods of Computation 12.20 Approximations

§12.19 Tables

Keywords:: parabolic cylinder functions
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Abramowitz and Stegun (1964, Chapter 19) includes $\mathop{U\/}\nolimits\!\left(a,x\right)$ and $\mathop{V\/}\nolimits\!\left(a,x\right)$ for $\pm a=0(.1)1(.5)5$ , , 5S; $\mathop{W\/}\nolimits\!\left(a,\pm x\right)$ for $\pm a=0(.1)1(1)5$ , , 4-5D or 4-5S.
Miller (1955) includes $\mathop{W\/}\nolimits\!\left(a,x\right)$ , $\mathop{W\/}\nolimits\!\left(a,-x\right)$ , and reduced derivatives for , , 8D or 8S. Modulus and phase functions, and also other auxiliary functions are tabulated.
Fox (1960) includes modulus and phase functions for $\mathop{W\/}\nolimits\!\left(a,x\right)$ and $\mathop{W\/}\nolimits\!\left(a,-x\right)$ , and several auxiliary functions for $x^{{-1}}=0(.005)0.1$ , , 8S.
Kireyeva and Karpov (1961) includes $\mathop{D_{{p}}\/}\nolimits\!\left(x(1+i)\right)$ for $\pm x=0(.1)5$ , , and $\pm x=5(.01)10$ , , 7D.
Karpov and Čistova (1964) includes $\mathop{D_{{p}}\/}\nolimits\!\left(x\right)$ for , $\pm x=0(.01)5$ ; , $\pm x=5(.01)10$ , 6D.
Karpov and Čistova (1968) includes $e^{{-\frac{1}{4}x^{2}}}\mathop{D_{{p}}\/}\nolimits\!\left(-x\right)$ and $e^{{-\frac{1}{4}x^{2}}}\mathop{D_{{p}}\/}\nolimits\!\left(ix\right)$ for and $x^{{-1}}$ = 0(.001 or .0001)5, , 7D or 8S.
Murzewski and Sowa (1972) includes $\mathop{D_{{-n}}\/}\nolimits\!\left(x\right)$ $\left(=\mathop{U\/}\nolimits\!\left(n-\tfrac{1}{2},x\right)\right)$ for , , 7S.
Zhang and Jin (1996, pp. 455–473) includes $\mathop{U\/}\nolimits\!\left(\pm n-\frac{1}{2},x\right)$ , $\mathop{V\/}\nolimits\!\left(\pm n-\frac{1}{2},x\right)$ , $\mathop{U\/}\nolimits\!\left(\pm\nu-\frac{1}{2},x\right)$ , $\mathop{V\/}\nolimits\!\left(\pm\nu-\frac{1}{2},x\right)$ , and derivatives, $\nu=n+\frac{1}{2}$ , , , 8S; $\mathop{W\/}\nolimits\!\left(a,\pm x\right)$ , $\mathop{W\/}\nolimits\!\left(-a,\pm x\right)$ , and derivatives, , and , , , 8S. Also, first zeros of $\mathop{U\/}\nolimits\!\left(a,x\right)$ , $\mathop{V\/}\nolimits\!\left(a,x\right)$ , and of derivatives, , 6D; first three zeros of $\mathop{W\/}\nolimits\!\left(a,-x\right)$ and of derivative, , 6D; first three zeros of $\mathop{W\/}\nolimits\!\left(-a,\pm x\right)$ and of derivative, , 6D; real and imaginary parts of $\mathop{U\/}\nolimits\!\left(a,z\right)$ , , , , , 8S.