table%20of

SearchAdvancedHelp

(0.001 seconds)

21—30 of 50 matching pages

21: 26.5 Lattice Paths: Catalan Numbers

… ►See Table 26.5.1. ►

Table 26.5.1: Catalan numbers.

► ►►►

$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
…
6	132	13	7 42900	20	65641 20420

►

…

22: 24.2 Definitions and Generating Functions

… ►

§24.2(iv) Tables

►

Table 24.2.1: Bernoulli and Euler numbers.

► ►►

$n$	$B_n$	$E_n$
…

►

►

Table 24.2.2: Bernoulli and Euler polynomials.

► ►►

$n$	$B_n\left(x\right)$	$E_n\left(x\right)$
…

►

…

23: 5.22 Tables

§5.22 Tables

… ►For early tables for both real and complex variables see Fletcher et al. (1962), Lebedev and Fedorova (1960), and Luke (1975, p. 21). ►

§5.22(ii) Real Variables

►Abramowitz and Stegun (1964, Chapter 6) tabulates $\mathrm{\Gamma }\left(x\right)$, $\ln \mathrm{\Gamma }\left(x\right)$, $\psi \left(x\right)$, and ${\psi }^{\prime }\left(x\right)$ for $x=1(.005)2$ to 10D; ${\psi }^{\prime \prime }\left(x\right)$ and ${\psi }^{(3)}\left(x\right)$ for $x=1(.01)2$ to 10D; $\mathrm{\Gamma }\left(n\right)$, $1/\mathrm{\Gamma }\left(n\right)$, $\mathrm{\Gamma }\left(n+\frac{1}{2}\right)$, $\psi \left(n\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{1}{3}\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{1}{2}\right)$, and ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{2}{3}\right)$ for $n=1(1)101$ to 8–11S; $\mathrm{\Gamma }\left(n+1\right)$ for $n=100(100)1000$ to 20S. … ►

§5.22(iii) Complex Variables

…

24: 25.6 Integer Arguments

… ►

25.6.3 $$\zeta \left(-n\right)=-\frac{B_{n+1}}{n+1},$$ $n=1,2,3,\mathrm{\dots }$.

ⓘ

Symbols:

$B_n$: Bernoulli numbers, $\zeta \left(s\right)$: Riemann zeta function and $n$: nonnegative integer

Source:

Apostol (1976, (20), p. 266); with $n\ne 0$

A&S Ref:

23.2.15 (in slightly different form)

Permalink:

http://dlmf.nist.gov/25.6.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §25.6(i), §25.6 and Ch.25

…

25: Bibliography G

… ►

Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

ⓘ

Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

Encodings:

BibTeX

… ►

Number-Divisor Tables. British Association Mathematical Tables, Vol. VIII, Cambridge University Press, Cambridge, England.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

… ►

Tables of Partitions. Royal Society Math. Tables, Vol. 4, Cambridge University Press.

ⓘ

External Links:

ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

►

A table of partitions. Proc. London Math. Soc. (2) 39, pp. 142–149.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

►

A table of partitions (II). Proc. London Math. Soc. (2) 42, pp. 546–549.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

…

26: 26.9 Integer Partitions: Restricted Number and Part Size

… ►See Table 26.9.1. … ►

Table 26.9.1: Partitions $p_k\left(n\right)$.

► ►►►

$n$	$k$
	…
8	0	1	5	10	15	18	20	21	22	22	22
…

►

…

27: 3.4 Differentiation

… ►

$$B_{-2}^5=\frac{1}{120}(6-10t-15t^2+20t^3-5t^4),$$

… ►

$$B_{-3}^6=-\frac{1}{720}(12-8t-45t^2+20t^3+15t^4-6t^5),$$

… ►For corresponding formulas for second, third, and fourth derivatives, with $t=0$, see Collatz (1960, Table III, pp. 538–539). … ►The results in this subsection for the partial derivatives follow from Panow (1955, Table 10). … ►For additional formulas involving values of ${\nabla }^{2}u$ and ${\nabla }^{4}u$ on square, triangular, and cubic grids, see Collatz (1960, Table VI, pp. 542–546). …

28: Bibliography

… ►

Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

ⓘ

External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

BibTeX

… ►

On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

ⓘ

External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

BibTeX

… ►

Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

Encodings:

BibTeX

… ►

Table of Definite and Infinite Integrals. Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.

ⓘ

Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1386.

External Links:

ISBN 0-444-42151-3, MathReview (R. P. Boas), ZentralBlatt

Referenced by:

§1.4(iv), §10.22(vi), §10.43(vi), §11.7(v), §11.9(iv), §12.5(iv), §13.10(vi), §13.23(v), §15.14, §16.20, §16.5, §18.17(ix), §4.10(iii), §4.26(v), §4.40(v), §5.13, §6.14(iii), §7.14(iii), §8.14, §8.19(x).

Encodings:

BibTeX

… ►

Tables of Lamé Polynomials. Pergamon Press, The Macmillan Co., New York.

ⓘ

External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§29.15(ii), 2nd item.

Encodings:

BibTeX

…

29: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions

… ►Table 26.4.1 gives numerical values of multinomials and partitions $\lambda ,M_1,M_2,M_3$ for $1\le m\le n\le 5$. … ►

Table 26.4.1: Multinomials and partitions.

► ►►►►

$n$	$m$	$\lambda$	$M_1$	$M_2$	$M_3$
…
$5$	$2$	$2^1,3^1$	$10$	$20$	$10$
$5$	$3$	$1^2,3^1$	$20$	$20$	$10$
…

►

…

30: Bibliography K

… ►

Auxiliary table for the incomplete elliptic integrals. J. Math. Physics 27, pp. 11–36.

ⓘ

External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§19.12.

Encodings:

BibTeX

… ►

Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

ⓘ

External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

… ►

Tables of Weber functions. Vol. I. Mathematical Tables Series, Vol. 15, Pergamon Press, London-New York.

ⓘ

Notes:

Translated by Prasenjit Basu

External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

4th item.

Encodings:

BibTeX

… ►

Tables of values of the modified Mathieu functions. Math. Comp. 14, pp. 118–129.

ⓘ

External Links:

FullText, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

5th item.

Encodings:

BibTeX

…