# §7.23 Tables

## §7.23(i) Introduction

Lebedev and Fedorova (1960) and Fletcher et al. (1962) give comprehensive indexes of mathematical tables. This section lists relevant tables that appeared later.

## §7.23(ii) Real Variables

• Abramowitz and Stegun (1964, Chapter 7) includes $\mathop{\mathrm{erf}\/}\nolimits x$, $(2/\sqrt{\pi})e^{-x^{2}}$, $x\in[0,2]$, 10D; $(2/\sqrt{\pi})e^{-x^{2}}$, $x\in[2,10]$, 8S; $xe^{x^{2}}\mathop{\mathrm{erfc}\/}\nolimits x$, $x^{-2}\in[0,0.25]$, 7D; $2^{n}\mathop{\Gamma\/}\nolimits\!\left(\frac{1}{2}n+1\right)\mathop{\mathrm{i}% ^{n}\mathrm{erfc}\/}\nolimits\!\left(x\right)$, $n=1(1)6,10,11$, $x\in[0,5]$, 6S; $\mathop{F\/}\nolimits\!\left(x\right)$, $x\in[0,2]$, 10D; $x\mathop{F\/}\nolimits\!\left(x\right)$, $x^{-2}\in[0,0.25]$, 9D; $\mathop{C\/}\nolimits\!\left(x\right)$, $\mathop{S\/}\nolimits\!\left(x\right)$, $x\in[0,5]$, 7D; $\mathop{\mathrm{f}\/}\nolimits\!\left(x\right)$, $\mathop{\mathrm{g}\/}\nolimits\!\left(x\right)$, $x\in[0,1]$, $x^{-1}\in[0,1]$, 15D.

• Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral $\mathop{G\/}\nolimits\!\left(x\right)$, $x=1(.1)3(.5)8$, 4D; also $\mathop{G\/}\nolimits\!\left(x\right)+\mathop{\ln\/}\nolimits x$, $x=0(.05)1$, 4D.

• Finn and Mugglestone (1965) includes the Voigt function $\mathop{H\/}\nolimits\!\left(a,u\right)$, $u\in[0,22]$, $a\in[0,1]$, 6S.

• Zhang and Jin (1996, pp. 637, 639) includes $(2/\sqrt{\pi})e^{-x^{2}}$, $\mathop{\mathrm{erf}\/}\nolimits x$, $x=0(.02)1(.04)3$, 8D; $\mathop{C\/}\nolimits\!\left(x\right)$, $\mathop{S\/}\nolimits\!\left(x\right)$, $x=0(.2)10(2)100(100)500$, 8D.

## §7.23(iii) Complex Variables, $z=x+iy$

• Abramowitz and Stegun (1964, Chapter 7) includes $\mathop{w\/}\nolimits\!\left(z\right)$, $x=0(.1)3.9$, $y=0(.1)3$, 6D.

• Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of $\mathop{\mathrm{erf}\/}\nolimits z$, $x\in[0,5]$, $y=0.5(.5)3$, 7D and 8D, respectively; the real and imaginary parts of $\int_{x}^{\infty}e^{\pm\mathrm{i}t^{2}}\mathrm{d}t$, $(1/\sqrt{\pi})e^{\mp\mathrm{i}(x^{2}+(\pi/4))}\int_{x}^{\infty}e^{\pm\mathrm{i% }t^{2}}\mathrm{d}t$, $x=0(.5)20(1)25$, 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.

## §7.23(iv) Zeros

• Fettis et al. (1973) gives the first 100 zeros of $\mathop{\mathrm{erf}\/}\nolimits z$ and $\mathop{w\/}\nolimits\!\left(z\right)$ (the table on page 406 of this reference is for $\mathop{w\/}\nolimits\!\left(z\right)$, not for $\mathop{\mathrm{erfc}\/}\nolimits z$), 11S.

• Zhang and Jin (1996, p. 642) includes the first 10 zeros of $\mathop{\mathrm{erf}\/}\nolimits z$, 9D; the first 25 distinct zeros of $\mathop{C\/}\nolimits\!\left(z\right)$ and $\mathop{S\/}\nolimits\!\left(z\right)$, 8S.