DLMF: GA.22 Tables

§GA.22. Tables

Keywords:: gamma function

§GA.22(i)Introduction
§GA.22(ii)Real Variables
§GA.22(iii)Complex Variables

§GA.22(i). Introduction

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).

§GA.22(ii). Real Variables

Abramowitz and Stegun(1964)(Chapter 6) tabulates $\Gamma\!\left(x\right)$ , $\mathrm{ln}\Gamma\!\left(x\right)$ , $\psi\!\left(x\right)$ , 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 $\Gamma\!\left(x\right)$ , $\ifrac{1}{\Gamma\!\left(x\right)}$ , $\Gamma\!\left(-x\right)$ , $\mathrm{ln}\Gamma\!\left(x\right)$ , $\psi\!\left(x\right)$ , $\psi\!\left(-x\right)$ , ${{\psi}^{{\prime}}}\!\left(x\right)$ , 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.

§GA.22(iii). Complex Variables

Abramov(1960) tabulates $\mathrm{ln}\Gamma\!\left(x+iy\right)$ for $x=1$ ( $.01$ ) $2$ , $y=0$ ( $.01$ ) $4$ to 6D. Abramowitz and Stegun(1964)(Chapter 6) tabulates $\mathrm{ln}\Gamma\!\left(x+iy\right)$ 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 $\Gamma\!\left(x+iy\right)$ , $\mathrm{ln}\Gamma\!\left(x+iy\right)$ , and $\psi\!\left(x+iy\right)$ for $x=0.5,1,5,10$ , $y=0(.5)10$ to 8S.

§GA.22. Tables

Contents

§GA.22(i). Introduction

§GA.22(ii). Real Variables

§GA.22(iii). Complex Variables