§ 5.22. Tables

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§5.22(i)Introduction
§5.22(ii)Real Variables
§5.22(iii)Complex Variables

§ 5.22(i). Introduction

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In this section and §5.23 the notations 8S and 8D signify 8 significant figures and 8 decimal places, respectively.

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

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

§ 5.22(iii). Complex Variables

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

§ 5.22. Tables

Contents

§ 5.22(i). Introduction

§ 5.22(ii). Real Variables

§ 5.22(iii). Complex Variables