# §12.19 Tables

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

• Miller (1955) includes $W\left(a,x\right)$, $W\left(a,-x\right)$, 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 $W\left(a,x\right)$ and $W\left(a,-x\right)$, and several auxiliary functions for $x^{-1}=0(.005)0.1$, $a=-10(1)10$, 8S.

• Kireyeva and Karpov (1961) includes $D_{p}\left(x(1+i)\right)$ for $\pm x=0(.1)5$, $p=0(.1)2$, and $\pm x=5(.01)10$, $p=0(.5)2$, 7D.

• Karpov and Čistova (1964) includes $D_{p}\left(x\right)$ for $p=-2(.1)0$, $\pm x=0(.01)5$; $p=-2(.05)0$, $\pm x=5(.01)10$, 6D.

• Karpov and Čistova (1968) includes $e^{-\frac{1}{4}x^{2}}D_{p}\left(-x\right)$ and $e^{-\frac{1}{4}x^{2}}D_{p}\left(ix\right)$ 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 $D_{-n}\left(x\right)$ $\left(=U\left(n-\tfrac{1}{2},x\right)\right)$ for $n=1(1)20$, $x=0(.05)3$, 7S.

• Zhang and Jin (1996, pp. 455–473) includes $U\left(\pm n-\frac{1}{2},x\right)$, $V\left(\pm n-\frac{1}{2},x\right)$, $U\left(\pm\nu-\frac{1}{2},x\right)$, $V\left(\pm\nu-\frac{1}{2},x\right)$, and derivatives, $\nu=n+\frac{1}{2}$, $n=0(1)10(10)30$, $x=0.5,1,5,10,30,50$, 8S; $W\left(a,\pm x\right)$, $W\left(-a,\pm x\right)$, 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 $U\left(a,x\right)$, $V\left(a,x\right)$, and of derivatives, $a=-6(.5){-1}$, 6D; first three zeros of $W\left(a,-x\right)$ and of derivative, $a=0(.5)4$, 6D; first three zeros of $W\left(-a,\pm x\right)$ and of derivative, $a=0.5(.5)5.5$, 6D; real and imaginary parts of $U\left(a,z\right)$, $a=-1.5(1)1.5$, $z=x+iy$, $x=0.5,1,5,10$, $y=0(.5)10$, 8S.

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