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►Extensive numerical tables of all the elementary functions for real values of their arguments appear in Abramowitz and Stegun (1964, Chapter 4). This handbook also includes lists of references for earlier tables, as do Fletcher et al. (1962) and Lebedev and Fedorova (1960). …

13: 10.75 Tables

§10.75 Tables

… ►

•

The main tables in Abramowitz and Stegun (1964, Chapter 9) give $J_{0}\left(x\right)$ to 15D, $J_{1}\left(x\right)$ , $J_{2}\left(x\right)$ , $Y_{0}\left(x\right)$ , $Y_{1}\left(x\right)$ to 10D, $Y_{2}\left(x\right)$ to 8D, $x=0(.1)17.5$ ; $Y_{n}\left(x\right)-(2/\pi)J_{n}\left(x\right)\ln x$ , $n=0,1$ , $x=0(.1)2$ , 8D; $J_{n}\left(x\right)$ , $Y_{n}\left(x\right)$ , $n=3(1)9$ , $x=0(.2)20$ , 5D or 5S; $J_{n}\left(x\right)$ , $Y_{n}\left(x\right)$ , $n=0(1)20(10)50,100$ , $x=1,2,5,10,50,100$ , 10S; modulus and phase functions $\sqrt{x}M_{n}\left(x\right)$ , $\theta_{n}\left(x\right)-x$ , $n=0,1,2$ , $\ifrac{1}{x}=0(.01)0.1$ , 8D.

… ►

•

The main tables in Abramowitz and Stegun (1964, Chapter 9) give $e^{-x}I_{n}\left(x\right)$ , $e^{x}K_{n}\left(x\right)$ , $n=0,1,2$ , $x=0(.1)10(.2)20$ , 8D–10D or 10S; $\sqrt{x}e^{-x}I_{n}\left(x\right)$ , $(\sqrt{x}/\pi)$ $e^{x}K_{n}\left(x\right)$ , $n=0,1,2$ , $1/x=0(.002)0.05$ ; $K_{0}\left(x\right)+I_{0}\left(x\right)\ln x$ , $x(K_{1}\left(x\right)-I_{1}\left(x\right)\ln x)$ , $x=0(.1)2$ , 8D; $e^{-x}I_{n}\left(x\right)$ , $e^{x}K_{n}\left(x\right)$ , $n=3(1)9$ , $x=0(.2)10(.5)20$ , 5S; $I_{n}\left(x\right)$ , $K_{n}\left(x\right)$ , $n=0(1)20(10)50,100$ , $x=1,2,5,10,50,100$ , 9–10S.

… ►

•

The main tables in Abramowitz and Stegun (1964, Chapter 10) give $\mathsf{j}_{n}\left(x\right)$ , $\mathsf{y}_{n}\left(x\right)$ $n=0(1)8$ , $x=0(.1)10$ , 5–8S; $\mathsf{j}_{n}\left(x\right)$ , $\mathsf{y}_{n}\left(x\right)$ $n=0(1)20(10)50$ , 100, $x=1,2,5,10,50,100$ , 10S; ${\mathsf{i}^{(1)}_{n}}\left(x\right)$ , $\mathsf{k}_{n}\left(x\right)$ , $n=0,1,2$ , $x=0(.1)5$ , 4–9D; ${\mathsf{i}^{(1)}_{n}}\left(x\right)$ , $\mathsf{k}_{n}\left(x\right)$ , $n=0(1)20(10)50$ , 100, $x=1,2,5,10,50,100$ , 10S. (For the notation see §10.1 and §10.47(ii).)

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Olver (1960) tabulates $a^{\prime}_{n,m}$ , $\mathsf{j}_{n}\left(a^{\prime}_{n,m}\right)$ , $b^{\prime}_{n,m}$ , $\mathsf{y}_{n}\left(b^{\prime}_{n,m}\right)$ , $n=1(1)20$ , $m=1(1)50$ , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as $n\to\infty$ .

…

14: 26.2 Basic Definitions

… ►See Table 26.2.1 for

n=0(1)50

. For the actual partitions (

\pi

) for

n=1(1)5

see Table 26.4.1. … ►

Table 26.2.1: Partitions

p\left(n\right)

► ►►►

$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
…
3	3	20	627	37	21637
…

►

15: 26.3 Lattice Paths: Binomial Coefficients

… ►For numerical values of

\genfrac{(}{)}{0.0pt}{}{m}{n}

and

\genfrac{(}{)}{0.0pt}{}{m+n}{n}

see Tables 26.3.1 and 26.3.2. ►

Table 26.3.1: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m}{n}

► ►►

$m$	$n$
$m$	…

► ►

Table 26.3.2: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m+n}{m}

for lattice paths.

► ►►

$m$	$n$
$m$	…

► …

16: 11.14 Tables

§11.14 Tables

… ►For tables before 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960). Tables listed in these Indices are omitted from the subsections that follow. ►

§11.14(ii) Struve Functions

… ►

§11.14(iv) Anger–Weber Functions

…

17: 27.2 Functions

… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. Tables of primes (§27.21) reveal great irregularity in their distribution. … ►

§27.2(ii) Tables

►Table 27.2.1 lists the first 100 prime numbers

p_{n}

. Table 27.2.2 tabulates the Euler totient function

\phi\left(n\right)

, the divisor function

d\left(n\right)

(

=\sigma_{0}(n)

), and the sum of the divisors

\sigma(n)

(

=\sigma_{1}(n)

), for

n=1(1)52

. …

18: 20 Theta Functions

Chapter 20 Theta Functions

…

19: 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. ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts

\not\equiv\pm 2\pmod{5}

, partitions into parts

\not\equiv\pm 1\pmod{5}

, and unrestricted plane partitions up to 100. It also contains a table of Gaussian polynomials up to

\genfrac{[}{]}{0.0pt}{}{12}{6}_{q}

. ►Goldberg et al. (1976) contains tables of binomial coefficients to

n=100

and Stirling numbers to

n=40

20: 12.19 Tables

§12.19 Tables

… ►

•

Murzewski and Sowa (1972) includes $D_{-n}\left(x\right)$ $\left(=U\left(n-\tfrac{1}{2},x\right)\right)$ for $n=1(1)20$ , $x=0(.05)3$ , 7S.

… ►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

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11—20 of 229 matching pages

11: 9.18 Tables

§9.18 Tables

§9.18(ii) Real Variables

§9.18(iii) Complex Variables

§9.18(iv) Zeros

§9.18(v) Integrals

12: 4.46 Tables

§4.46 Tables