§25.19 Tables

Keywords:: Clausen’s integral, Dirichlet -functions, Fermi–Dirac integrals, Hurwitz zeta function, Riemann–Siegel formula, Riemann zeta function, dilogarithms, polylogarithms
Permalink:: http://dlmf.nist.gov/25.19

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