.世界杯决赛32『网址:mxsty.cc』.微博世界杯榜-m4x5s2-2022年11月29日2时45分15秒

SearchAdvancedHelp

(0.002 seconds)

21—30 of 208 matching pages

21: 26.12 Plane Partitions

… ►

Table 26.12.1: Plane partitions.

► ►►►►►

$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$	$n$	$\mathrm{pp}\left(n\right)$
…
11	859	28	24 83234	45	17740 79109
12	1479	29	37 59612	46	25435 35902
…
15	6879	32	127 33429	49	73910 26522
…

►

… ►

26.12.26 $$\mathrm{pp}\left(n\right)\sim \frac{{\left(\zeta \left(3\right)\right)}^{7/36}}{2^{11/36}{(3\pi )}^{1/2}{n}^{25/36}}\exp \left(3{\left(\zeta \left(3\right)\right)}^{1/3}{\left(\frac{1}{2}n\right)}^{2/3}+{\zeta }^{\prime }\left(-1\right)\right),$$

ⓘ

Symbols:

$\zeta \left(s\right)$: Riemann zeta function, $\sim$: asymptotic equality, $\exp z$: exponential function, $\mathrm{pp}\left(n\right)$: number of plane partitions of $n$ , $n$: nonnegative integer and $\pi$: plane partition

Referenced by:

§26.12(iv), Erratum (V1.0.5) for Equation (26.12.26)

Permalink:

http://dlmf.nist.gov/26.12.E26

Encodings:

pMML, png, TeX

Errata (effective with 1.0.5):

The original statement of this equation, $\mathrm{pp}\left(n\right)\sim {\left(\frac{\zeta \left(3\right)}{2^{11}{n}^{25}}\right)}^{1/36}\exp \left(3{\left(\frac{\zeta \left(3\right)n^2}{4}\right)}^{1/3}+{\zeta }^{\prime }\left(-1\right)\right)$, has been corrected.

Reported 2011-09-05 by Suresh Govindarajan

See also:

Annotations for §26.12(iv), §26.12 and Ch.26

…

22: Bibliography C

… ►

Determination of $\nu$-zeros of Hankel functions. Comput. Phys. Comm. 32 (3), pp. 333–339.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 7S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Some inequalities for hypergeometric functions. Proc. Amer. Math. Soc. 17 (1), pp. 32–39.

ⓘ

External Links:

FullText, MathReview (Gabor Szegő), ZentralBlatt

Referenced by:

§19.24(i), §19.24(i), §19.24(ii), §19.9(i), §19.9(ii).

Encodings:

BibTeX

… ►

Asymptotics of Racah coefficients and polynomials. J. Phys. A 32 (3), pp. 537–553.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§34.8, §34.8.

Encodings:

BibTeX

… ►

A dispersion analysis for difference schemes: Tables of generalized Airy functions. Math. Comp. 32 (144), pp. 1163–1170.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (Philip Brenner), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

… ►

Gauss and the arithmetic-geometric mean. Notices Amer. Math. Soc. 32 (2), pp. 147–151.

ⓘ

External Links:

ISSN 0002-9920, MathReview (Willard Parker)

Referenced by:

§19.8(i).

Encodings:

BibTeX

…

23: Bibliography M

… ►

Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd edition, Springer-Verlag, New York-Berlin.

ⓘ

Notes:

Table errata: Math. Comp. v. 23 (1969), p. 471, v. 24 (1970), pp. 240 and 505, v. 25 (1971), no. 113, p. 201, v. 29 (1975), no. 130, p. 672, v. 30 (1976), no. 135, pp. 677–678, v. 32 (1978), no. 141, pp. 319–320, v. 36 (1981), no. 153, pp. 315–317, v. 41 (1983), no. 164, pp. 775–776, and v. 81 (2012), no. 280, p. 2251

External Links:

MathReview (Mary L. Boas), ZentralBlatt

Referenced by:

§10.15, §10.22(vi), §10.32(iv), §10.38, §10.43(vi), §10.60(iv), §10.9(iv), §11.5(iii), Ch.11, §12.12, §12.5(iv), Ch.12, §13.10(vi), §13.23(iv), §14.1, §14.11, §14.12(ii), §14.18(iv), §14.25, §14.3(iii), §14.5(v), §14.7(iv), Ch.14, (25.5.21), §25.5, (25.6.1), (25.6.2), §25.6(i), §8.1, Notations B, Notations I, Notations P, Notations P, Notations Q, Notations Q.

Encodings:

BibTeX

… ►

On the evaluation of the integral over the product of two spherical Bessel functions. J. Math. Phys. 32 (3), pp. 642–648.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (S. K. Chatterjea), ZentralBlatt

Referenced by:

§1.17(ii), §10.59.

Encodings:

BibTeX

… ►

Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions. Math. Nachr. 32, pp. 49–62.

ⓘ

External Links:

Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§29.11, §29.7(ii).

Encodings:

BibTeX

►

On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.

ⓘ

External Links:

Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.11, §29.7(ii).

Encodings:

BibTeX

… ►

Rational solutions of the second and the fourth Painlevé equations. Funkcial. Ekvac. 28 (1), pp. 1–32.

ⓘ

External Links:

ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.8(iv).

Encodings:

BibTeX

…

24: Bibliography B

… ►

Zeros of generalized Airy functions. Mathematika 32 (1), pp. 104–117.

ⓘ

External Links:

ISSN 0025-5793, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

… ►

Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

ⓘ

External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§8.7.

Encodings:

BibTeX

… ►

A monotonicity property involving ${}_3{}^{}F_2^{}$ and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.

ⓘ

External Links:

ISSN 1095-7154, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§19.9(i), §19.9(i).

Encodings:

BibTeX

… ►

Vortices in Ginzburg-Landau Equations. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), pp. 11–19.

ⓘ

External Links:

ISSN 1431-0643, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§17.17.

Encodings:

BibTeX

… ►

Rational Chebyshev approximations for the Bickley functions $K{i}_n(x)$ . Math. Comp. 32 (143), pp. 876–886.

ⓘ

External Links:

ISSN 0025-5718, FullText, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§10.76(iii).

Encodings:

BibTeX

…

25: 30.9 Asymptotic Approximations and Expansions

… ►

$2^6{\beta }_1=-q^3-11q+32m^{2}q,$

… ►

$$2^{20}{\beta }_5=-527q^7-61529q^5-\mathrm{10\hspace{0.33em}43961}{q}^3-\mathrm{22\hspace{0.33em}41599}q+32m^2(5739q^5+\mathrm{1\hspace{0.33em}27550}{q}^3+\mathrm{2\hspace{0.33em}98951}q)-2048m^4(355q^3+1505q)+65536m^{6}q.$$

…

26: Bibliography S

… ►

Chebyshev expansions for the error and related functions. Math. Comp. 32 (144), pp. 1232–1240.

ⓘ

External Links:

FullText, Document, MathReview (L. Fox), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

… ►

The accuracy of iterated JWBK approximations for Coulomb radial functions. Comput. Phys. Comm. 32 (2), pp. 115–119.

ⓘ

External Links:

Document

Referenced by:

§33.23(vii).

Encodings:

BibTeX

… ►

The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.

ⓘ

External Links:

ISSN 0253-424X, MathReview

Referenced by:

§9.10(v).

Encodings:

BibTeX

… ►

Elliptic Solitons and Heun’s Equation. In The Kowalevski Property (Leeds, UK, 2000), V. B. Kuznetsov (Ed.), CRM Proc. Lecture Notes, Vol. 32, pp. 287–306.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§31.8.

Encodings:

BibTeX

… ►

Effective calculation of the incomplete gamma function for parameter values $\alpha =(2n+1)/2$, $n=0,\mathrm{\dots },5$ . Angew. Informatik 17, pp. 30–32.

ⓘ

Notes:

Includes Fortran code.

External Links:

ZentralBlatt

Referenced by:

§8.28(ii).

Encodings:

BibTeX

…

27: Peter A. Clarkson

… ►

32 Painlevé Transcendents

…

28: Bibliography F

… ►

Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

ⓘ

Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

External Links:

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

Referenced by:

3rd item, 2nd item, 1st item.

Encodings:

BibTeX

… ►

Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (Shao-Ming Fei), ZentralBlatt

Referenced by:

§13.3(ii), §15.5(i), §16.3(i).

Encodings:

BibTeX

… ►

On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.13(i), §32.7(i), §32.7(iii).

Encodings:

BibTeX

… ►

Application of the $\tau$-function theory of Painlevé equations to random matrices: ${\mathrm{P}}_{\mathrm{VI}}$, the JUE, CyUE, cJUE and scaled limits. Nagoya Math. J. 174, pp. 29–114.

ⓘ

External Links:

ISSN 0027-7630, MathReview, ZentralBlatt

Referenced by:

§32.10(vi), §32.6(v).

Encodings:

BibTeX

… ►

Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

ⓘ

Notes:

Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.

External Links:

ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(ii).

Encodings:

BibTeX

…

29: Bibliography D

… ►

Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. Sci. Math. (2) 28, pp. 29–32 (French).

ⓘ

External Links:

ZentralBlatt

Referenced by:

§24.1.

Encodings:

BibTeX

… ►

An approximation for ${\int }_{\chi }^{\mathrm{\infty }}{e}^{-t^2/2}{t}^p𝑑t,$ $\chi >0,$ $p$ real. Math. Comp. 32 (141), pp. 271–275.

ⓘ

External Links:

FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).

ⓘ

Notes:

With an appendix by I. M. Krichever. In Russian. English translation: Russian Math. Surveys 36(1981), no. 2, pp. 11–92 (1982)

External Links:

ISSN 0042-1316, Document, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§21.1, §21.6(ii), §21.7(i), Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2, Ch.21, Notations T.

Encodings:

BibTeX

… ►

Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. SIAM J. Math. Anal. 32 (5), pp. 987–1013.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§10.49(ii), §18.34(iii).

Encodings:

BibTeX

… ►

The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.

ⓘ

External Links:

ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

Encodings:

BibTeX

…

30: 3.1 Arithmetics and Error Measures

… ►In the case of the normalized binary interchange formats, the representation of data for binary32 (previously single precision) ($N=32$, $p=24$, $E_{\min }=-126$, $E_{\max }=127$), binary64 (previously double precision) ($N=64$, $p=53$, $E_{\min }=-1022$, $E_{\max }=1023$) and binary128 (previously quad precision) ($N=128$, $p=113$, $E_{\min }=-16382$, $E_{\max }=16383$) are as in Figure 3.1.1. The respective machine precisions are $\frac{1}{2}{ϵ}_M=0.596\times {10}^{-7}$, $\frac{1}{2}{ϵ}_M=0.111\times {10}^{-15}$ and $\frac{1}{2}{ϵ}_M=0.963\times {10}^{-34}$. …