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5 Gamma FunctionComputation

§5.22 Tables

Contents

§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^{{\prime}}}\!\left(x\right) for x=1(.005)2 to 10D; {\mathop{\psi\/}\nolimits^{{\prime\prime}}}\!\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^{{\prime}}}\!\left(x\right), and {\mathop{\psi\/}\nolimits^{{\prime}}}\!\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.

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