# §5.22 Tables

## §5.22(i) Introduction

For early tables for both real and complex variables see Fletcher et al. (1962), Lebedev and Fedorova (1960), and Luke (1975, p. 21).

## §5.22(ii) Real Variables

Abramowitz and Stegun (1964, Chapter 6) tabulates $\mathop{\Gamma\/}\nolimits\!\left(x\right)$, $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x\right)$, $\mathop{\psi\/}\nolimits\!\left(x\right)$, and $\mathop{\psi\/}\nolimits'\!\left(x\right)$ for $x=1(.005)2$ to 10D; $\mathop{\psi\/}\nolimits''\!\left(x\right)$ and $\mathop{\psi^{(3)}\/}\nolimits\!\left(x\right)$ for $x=1(.01)2$ to 10D; $\mathop{\Gamma\/}\nolimits\!\left(n\right)$, $\ifrac{1}{\mathop{\Gamma\/}\nolimits\!\left(n\right)}$, $\mathop{\Gamma\/}\nolimits\!\left(n+\tfrac{1}{2}\right)$, $\mathop{\psi\/}\nolimits\!\left(n\right)$, $\mathop{\mathrm{log}_{10}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(n\right)$, $\mathop{\mathrm{log}_{10}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(n+% \tfrac{1}{3}\right)$, $\mathop{\mathrm{log}_{10}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(n+% \tfrac{1}{2}\right)$, and $\mathop{\mathrm{log}_{10}\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(n+% \tfrac{2}{3}\right)$ for $n=1(1)101$ to 8–11S; $\mathop{\Gamma\/}\nolimits\!\left(n+1\right)$ for $n=100(100)1000$ to 20S. Zhang and Jin (1996, pp. 67–69 and 72) tabulates $\mathop{\Gamma\/}\nolimits\!\left(x\right)$, $\ifrac{1}{\mathop{\Gamma\/}\nolimits\!\left(x\right)}$, $\mathop{\Gamma\/}\nolimits\!\left(-x\right)$, $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x\right)$, $\mathop{\psi\/}\nolimits\!\left(x\right)$, $\mathop{\psi\/}\nolimits\!\left(-x\right)$, $\mathop{\psi\/}\nolimits'\!\left(x\right)$, and $\mathop{\psi\/}\nolimits'\!\left(-x\right)$ for $x=0(.1)5$ to 8D or 8S; $\mathop{\Gamma\/}\nolimits\!\left(n+1\right)$ for $n=0(1)100(10)250(50)500(100)3000$ to 51S.

## §5.22(iii) Complex Variables

Abramov (1960) tabulates $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)$ for $x=1$ ($.01$) $2$, $y=0$ ($.01$) $4$ to 6D. Abramowitz and Stegun (1964, Chapter 6) tabulates $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)$ for $x=1$ ($.1$) $2$, $y=0$ ($.1$) $10$ to 12D. This reference also includes $\mathop{\psi\/}\nolimits\!\left(x+iy\right)$ for the same arguments to 5D. Zhang and Jin (1996, pp. 70, 71, and 73) tabulates the real and imaginary parts of $\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)$, $\mathop{\ln\/}\nolimits\mathop{\Gamma\/}\nolimits\!\left(x+iy\right)$, and $\mathop{\psi\/}\nolimits\!\left(x+iy\right)$ for $x=0.5,1,5,10$, $y=0(.5)10$ to 8S.