# tables of coefficients

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##### 1: 26.21 Tables
###### §26.21 Tables
Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients $\genfrac{(}{)}{0.0pt}{}{m}{n}$ for $m$ up to 50 and $n$ up to 25; extends Table 26.4.1 to $n=10$; tabulates Stirling numbers of the first and second kinds, $s\left(n,k\right)$ and $S\left(n,k\right)$, for $n$ up to 25 and $k$ up to $n$; tabulates partitions $p\left(n\right)$ and partitions into distinct parts $p\left(\mathcal{D},n\right)$ for $n$ up to 500. … Goldberg et al. (1976) contains tables of binomial coefficients to $n=100$ and Stirling numbers to $n=40$.
##### 3: 28.35 Tables
###### §28.35 Tables
• Ince (1932) includes eigenvalues $a_{n}$, $b_{n}$, and Fourier coefficients for $n=0$ or $1(1)6$, $q=0(1)10(2)20(4)40$; 7D. Also $\operatorname{ce}_{n}\left(x,q\right)$, $\operatorname{se}_{n}\left(x,q\right)$ for $q=0(1)10$, $x=1(1)90$, corresponding to the eigenvalues in the tables; 5D. Notation: $a_{n}=\mathit{be}_{n}-2q$, $b_{n}=\mathit{bo}_{n}-2q$.

• National Bureau of Standards (1967) includes the eigenvalues $a_{n}\left(q\right)$, $b_{n}\left(q\right)$ for $n=0(1)3$ with $q=0(.2)20(.5)37(1)100$, and $n=4(1)15$ with $q=0(2)100$; Fourier coefficients for $\operatorname{ce}_{n}\left(x,q\right)$ and $\operatorname{se}_{n}\left(x,q\right)$ for $n=0(1)15$, $n=1(1)15$, respectively, and various values of $q$ in the interval $[0,100]$; joining factors $g_{\mathit{e},n}(\sqrt{q})$, $f_{\mathit{e},n}(\sqrt{q})$ for $n=0(1)15$ with $q=0(.5\mbox{ to }10)100$ (but in a different notation). Also, eigenvalues for large values of $q$. Precision is generally 8D.

• Blanch and Clemm (1969) includes eigenvalues $a_{n}\left(q\right)$, $b_{n}\left(q\right)$ for $q=\rho e^{\mathrm{i}\phi}$, $\rho=0(.5)25$, $\phi=5^{\circ}(5^{\circ})90^{\circ}$, $n=0(1)15$; 4D. Also $a_{n}\left(q\right)$ and $b_{n}\left(q\right)$ for $q=\mathrm{i}\rho$, $\rho=0(.5)100$, $n=0(2)14$ and $n=2(2)16$, respectively; 8D. Double points for $n=0(1)15$; 8D. Graphs are included.

• ##### 4: 18.3 Definitions
For explicit power series coefficients up to $n=12$ for these polynomials and for coefficients up to $n=6$ for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). …
##### 6: 30.17 Tables
###### §30.17 Tables
• Flammer (1957) includes 18 tables of eigenvalues, expansion coefficients, spheroidal wave functions, and other related quantities. Precision varies between 4S and 10S.

• ##### 7: 18.25 Wilson Class: Definitions
Table 18.25.2 provides the leading coefficients $k_{n}$18.2(iii)) for the Wilson, continuous dual Hahn, Racah, and dual Hahn polynomials.
##### 9: 25.19 Tables
• 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.

• 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.