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31: 3.5 Quadrature

… ►Stroud and Secrest (1966) includes computational methods and extensive tables. … ►Tables 3.5.1–3.5.13 can be verified by application of the results given in the present subsection. …For the other classical OP’s see Table 3.5.17_5. … ►Extensive tables of quadrature nodes and weights can be found in Krylov and Skoblya (1985). … ►Using Table 3.5.18 we compute

g(t)

for

n=5

. …

32: 9 Airy and Related Functions

…

33: 26.6 Other Lattice Path Numbers

… ►See Table 26.6.1. ►

Table 26.6.1: Delannoy numbers

D(m,n)

► ►►

$m$	$n$
$m$	…

► … ►See Table 26.6.2. … ►See Table 26.6.3. … ►See Table 26.6.4. …

34: 18.3 Definitions

… ►

As eigenfunctions of second order differential operators (Bochner’s theorem, Bochner (1929)). See the differential equations $A(x)p_{n}^{\prime\prime}(x)+B(x)p_{n}^{\prime}(x)+\lambda_{n}p_{n}(x)=0$ , in Table 18.8.1.

… ►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. … ►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}\left(x,q\right)

\theta_{c}\left(x,q\right)

\theta_{d}\left(x,q\right)

\theta_{n}\left(x,q\right)

(see §20.1) and their logarithmic

x

-derivatives are given in Abramowitz and Stegun (1964, pp. 582–585) to 9D for

\varepsilon,\alpha=0(5^{\circ})90^{\circ}

, where (in radian measure)

\varepsilon=x/{\theta_{3}}^{2}\left(0,q\right)=\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}+iy_{n}

\operatorname{erf}z.

► ►►

$n$	$x_{n}$	$y_{n}$
…

► … ►Table 7.13.2 gives 10D values of the first five

x_{n}

and

y_{n}

. … ►

Table 7.13.2: Zeros

x_{n}+iy_{n}

\operatorname{erfc}z.

► ►►

$n$	$x_{n}$	$y_{n}$
…

► … ►Tables 7.13.3 and 7.13.4 give 10D values of the first five

x_{n}

and

y_{n}

C\left(z\right)

and

S\left(z\right)

, respectively. …

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). … ► ►