§25.19 Tables

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Keywords:: Clausen’s integral, Dirichlet $L$ -functions, Fermi–Dirac integrals, Hurwitz zeta function, Riemann zeta function, Riemann–Siegel formula, coefficients, dilogarithms, polylogarithms, tables
Permalink:: http://dlmf.nist.gov/25.19
See also:: Annotations for Ch.25

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Abramowitz and Stegun (1964) tabulates: $\zeta\left(n\right)$ , $n=2,3,4,\dots$ , 20D (p. 811); $\operatorname{Li}_{2}\left(1-x\right)$ , $x=0(.01)0.5$ , 9D (p. 1005); $f(\theta)$ , $\theta=15^{\circ}(1^{\circ})30^{\circ}(2^{\circ})90^{\circ}(5^{\circ})180^{\circ}$ , $f(\theta)+\theta\ln\theta$ , $\theta=0(1^{\circ})15^{\circ}$ , 6D (p. 1006). Here $f(\theta)$ denotes Clausen’s integral, given by the right-hand side of (25.12.9).
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Morris (1979) tabulates $\operatorname{Li}_{2}\left(x\right)$ (§25.12(i)) for $\pm x=0.02(.02)1(.1)6$ to 30D.
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Cloutman (1989) tabulates $\Gamma\left(s+1\right)F_{s}(x)$ , where $F_{s}(x)$ is the Fermi–Dirac integral (25.12.14), for $s=-\frac{1}{2},\frac{1}{2},\frac{3}{2},\frac{5}{2}$ , $x=-5(.05)25$ , to 12S.
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Fletcher et al. (1962, §22.1) lists many sources for earlier tables of $\zeta\left(s\right)$ for both real and complex $s$ . §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of $\zeta\left(s,a\right)$ , and §22.17 lists tables for some Dirichlet $L$ -functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.