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1: 11 Struve and Related Functions

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3: 12 Parabolic Cylinder Functions

Chapter 12 Parabolic Cylinder Functions

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$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$
…
2	1	2	3	15	8	4	24	28	12	6	56	41	40	2	42
…
8	4	4	15	21	12	4	32	34	16	4	54	47	46	2	48
…
10	4	4	18	23	22	2	24	36	12	9	91	49	42	3	57
11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
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13	12	2	14	26	12	4	42	39	24	4	56	52	24	6	98

5: 24.2 Definitions and Generating Functions

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Table 24.2.1: Bernoulli and Euler numbers.

► ►►►

$n$	$B_{n}$	$E_{n}$
…
$12$	$-\tfrac{691}{2730}$	$27\;02765$
…

► … ►

Table 24.2.3: Bernoulli numbers

B_{n}=N/D

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$n$	$N$	$D$	$B_{n}$
…
$12$	$-691$	$2730$	$-2.53113\;5531$	$\times 10^{-1}$
…

► ►

Table 24.2.4: Euler numbers

E_{n}

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$n$	$E_{n}$
…
$12$	$27\;02765$
…

► ►

Table 24.2.5: Coefficients

b_{n,k}

of the Bernoulli polynomials

B_{n}\left(x\right)=\sum_{k=0}^{n}b_{n,k}x^{k}

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…

► ►

Table 24.2.6: Coefficients

e_{n,k}

of the Euler polynomials

E_{n}\left(x\right)=\sum_{k=0}^{n}e_{n,k}x^{k}

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
…

►

6: 8.26 Tables

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•

Zhang and Jin (1996, Table 3.9) tabulates $I_{x}\left(a,b\right)$ for $x=0(.05)1$ , $a=0.5,1,3,5,10$ , $b=1,10$ to 8D.

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•

Abramowitz and Stegun (1964, pp. 245–248) tabulates $E_{n}\left(x\right)$ for $n=2,3,4,10,20$ , $x=0(.01)2$ to 7D; also $(x+n)e^{x}E_{n}\left(x\right)$ for $n=2,3,4,10,20$ , $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

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•

Pagurova (1961) tabulates $E_{n}\left(x\right)$ for $n=0(1)20$ , $x=0(.01)2(.1)10$ to 4-9S; $e^{x}E_{n}\left(x\right)$ for $n=2(1)10$ , $x=10(.1)20$ to 7D; $e^{x}E_{p}\left(x\right)$ for $p=0(.1)1$ , $x=0.01(.01)7(.05)12(.1)20$ to 7S or 7D.

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•

Stankiewicz (1968) tabulates $E_{n}\left(x\right)$ for $n=1(1)10$ , $x=0.01(.01)5$ to 7D.

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•

Zhang and Jin (1996, Table 19.1) tabulates $E_{n}\left(x\right)$ for $n=1,2,3,5,10,15,20$ , $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

7: 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. … ►It also contains a table of Gaussian polynomials up to

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

. …

8: 18.41 Tables

… ►Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates

T_{n}\left(x\right)

U_{n}\left(x\right)

L_{n}\left(x\right)

, and

H_{n}\left(x\right)

for

n=0(1)12

. The ranges of

x

are

0.2(.2)1

for

T_{n}\left(x\right)

and

U_{n}\left(x\right)

, and

0.5,1,3,5,10

for

L_{n}\left(x\right)

and

H_{n}\left(x\right)

. …

9: 26.10 Integer Partitions: Other Restrictions

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Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from

A_{j,k}

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	$p\left(\mathcal{D},n\right)$	$p\left(\mathcal{D}2,n\right)$	$p\left(\mathcal{D}2,\hbox{}\!\!\in\!T,n\right)$	$p\left(\mathcal{D}^{\prime}3,n\right)$
…
$10$	$10$	$6$	$4$	$4$
$11$	$12$	$7$	$4$	$5$
$12$	$15$	$9$	$6$	$6$
…
$14$	$22$	$12$	$8$	$8$
…
$17$	$38$	$19$	$12$	$12$
…