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31: 3.5 Quadrature

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Table 3.5.2: Nodes and weights for the 10-point Gauss–Legendre formula.

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$\pm x_k$	$w_k$
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Table 3.5.3: Nodes and weights for the 20-point Gauss–Legendre formula.

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$\pm x_k$	$w_k$
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Table 3.5.4: Nodes and weights for the 40-point Gauss–Legendre formula.

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$\pm x_k$	$w_k$
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Table 3.5.6: Nodes and weights for the 5-point Gauss–Laguerre formula.

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$x_k$		$w_k$
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Table 3.5.18: Nodes and weights for the 5-point complex Gauss quadrature formula with $s=1$.

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${\zeta }_k$				$w_k$
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32: 9 Airy and Related Functions

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33: 26.6 Other Lattice Path Numbers

… ►See Table 26.6.1. ►

Table 26.6.1: Delannoy numbers $D(m,n)$.

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$m$	$n$
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… ►See Table 26.6.2. … ►See Table 26.6.3. … ►See Table 26.6.4. …

34: 18.3 Definitions

… ►Table 18.3.1 provides the traditional definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and standardization (§§18.2(i) and 18.2(iii)). This table also includes the following special cases of Jacobi polynomials: ultraspherical, Chebyshev, and Legendre. ►

Table 18.3.1: Orthogonality properties for classical OP’s: intervals, weight functions, standardizations, leading coefficients, and parameter constraints. …

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Name	$p_n(x)$	$(a,b)$	$w(x)$	$h_n$	$k_n$	${\tilde{k}}_n/k_n$	Constraints
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… ►For representations of the polynomials in Table 18.3.1 by Rodrigues formulas, see §18.5(ii). …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). …

35: 20.15 Tables

§20.15 Tables

… ►Tables of Neville’s theta functions ${\theta }_s(x,q)$, ${\theta }_c(x,q)$, ${\theta }_d(x,q)$, ${\theta }_n(x,q)$ (see §20.1) and their logarithmic $x$-derivatives are given in Abramowitz and Stegun (1964, pp. 582–585) to 9D for $\epsilon ,\alpha =0(5^{\circ }){90}^{\circ }$, where (in radian measure) $\epsilon =x/{\theta }_3^2(0,q)=\pi x/(2K\left(k\right))$, and $\alpha$ is defined by (20.15.1). ►For other tables prior to 1961 see Fletcher et al. (1962, pp. 508–514) and Lebedev and Fedorova (1960, pp. 227–230).

36: 7.13 Zeros

… ►Table 7.13.1 gives 10D values of the first five $x_n$ and $y_n$. … ►

Table 7.13.1: Zeros $x_n+\mathrm{i}{y}_n$ of $\mathrm{erf}z.$

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$n$	$x_n$	$y_n$
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Table 7.13.2: Zeros $x_n+\mathrm{i}{y}_n$ of $\mathrm{erfc}z.$

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$n$	$x_n$	$y_n$
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Table 7.13.3: Complex zeros $x_n+\mathrm{i}{y}_n$ of $C\left(z\right).$

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$n$	$x_n$	$y_n$
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Table 7.13.4: Complex zeros $x_n+\mathrm{i}{y}_n$ of $S\left(z\right)$.

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$n$	$x_n$	$y_n$
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37: 19.37 Tables

§19.37 Tables

… ►Only tables published since 1960 are included. For earlier tables see Fletcher (1948), Lebedev and Fedorova (1960), and Fletcher et al. (1962). … ► ►

§19.37(iv) Symmetric Integrals

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38: 24.2 Definitions and Generating Functions

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§24.2(iv) Tables

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Table 24.2.1: Bernoulli and Euler numbers.

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$n$	$B_n$	$E_n$
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Table 24.2.2: Bernoulli and Euler polynomials.

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$n$	$B_n\left(x\right)$	$E_n\left(x\right)$
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39: 26.5 Lattice Paths: Catalan Numbers

… ►See Table 26.5.1. ►

Table 26.5.1: Catalan numbers.

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$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
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40: 36.7 Zeros

… ►The zeros in Table 36.7.1 are points in the $𝐱=(x,y)$ plane, where $\mathrm{ph}{\mathrm{\Psi }}_2\left(𝐱\right)$ is undetermined. … ►

Table 36.7.1: Zeros of cusp diffraction catastrophe to 5D.

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Zeros $\left\{\genfrac{}{}{0.0pt}{}{x}{y}\right\}$ inside, and zeros $\left[\genfrac{}{}{0.0pt}{}{x}{y}\right]$ outside, the cusp $x^2=\frac{8}{27}{|y|}^3$.
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