.1994年世界杯小组分组_『网址:68707.vip』2018世界杯直播咪咕_b5p6v3_2022年11月30日7时57分10秒_z9fzftt9n.cc

Did you mean .1994年世界杯小组分组_『网址:687.vii』2018世界杯直播咪咕_b5p6v3_2022年11月30日7时57分10秒_z9fzftt9n.cc ?

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1: Publications

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B. V. Saunders and Q. Wang (2005) Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

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Q. Wang and B. V. Saunders (2005) Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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A. Youssef (2007) Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007.

… ►

B. I. Schneider, B. R. Miller and B. V. Saunders (2018) NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53.

2: DLMF Project News

error generating summary

3: Bibliography N

… ►

G. Nemes (2018) Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions. Stud. Appl. Math. 140 (4), pp. 508–541.

ⓘ

External Links:: ISSN 0022-2526, Document, Link, MathReview (Pedro J. Pagola)
Referenced by:: §11.11(i), §11.11(i).
Encodings:: BibTeX

… ►

E. Neuman (1969a) Elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 99–102.

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Notes:: Includes Algol program.
External Links:: MathReview
Referenced by:: §19.39(iii).
Encodings:: BibTeX

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E. Neuman (1969b) On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

ⓘ

External Links:: MathReview, ZentralBlatt
Referenced by:: §19.36(ii).
Encodings:: BibTeX

… ►

V. Yu. Novokshënov (1985) The asymptotic behavior of the general real solution of the third Painlevé equation. Dokl. Akad. Nauk SSSR 283 (5), pp. 1161–1165 (Russian).

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Notes:: In Russian. English translation: Sov. Math., Dokl. 30(1988), no. 8, pp. 666–668.
External Links:: ISSN 0002-3264, MathReview (Vojislav Marić), ZentralBlatt
Referenced by:: §32.11(iv).
Encodings:: BibTeX

…

4: 27.12 Asymptotic Formulas: Primes

… ►

p_{n}

is the

n

th prime, beginning with

p_{1}=2

. … ►

27.12.1

\lim_{n\to\infty}\frac{p_{n}}{n\ln n}=1,

ⓘ

Symbols:: $\ln\NVar{z}$ : principal branch of logarithm function, $n$ : positive integer and $p,p_{1},\ldots$ : prime numbers
Permalink:: http://dlmf.nist.gov/27.12.E1
Encodings:: pMML, png, TeX
Change of Notation (effective with 1.0.10):: The notation for logarithm has been changed to $\ln$ from $\mathrm{log}$ .
See also:: Annotations for §27.12 and Ch.27

►

27.12.2

p_{n}>n\ln n,

n=1,2,\dots

ⓘ

Symbols:: $\ln\NVar{z}$ : principal branch of logarithm function, $n$ : positive integer and $p,p_{1},\ldots$ : prime numbers
Permalink:: http://dlmf.nist.gov/27.12.E2
Encodings:: pMML, png, TeX
Change of Notation (effective with 1.0.10):: The notation for logarithm has been changed to $\ln$ from $\mathrm{log}$ .
See also:: Annotations for §27.12 and Ch.27

►

27.12.3

\pi\left(x\right)=\left\lfloor x\right\rfloor-1-\sum_{p_{j}\leq\sqrt{x}}\left% \lfloor\frac{x}{p_{j}}\right\rfloor+\sum_{r\geq 2}(-1)^{r}\*\sum_{p_{j_{1}}<p_% {j_{2}}<\cdots<p_{j_{r}}\leq\sqrt{x}}\left\lfloor\frac{x}{p_{j_{1}}p_{j_{2}}% \cdots p_{j_{r}}}\right\rfloor,

x\geq 1

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Symbols:: $\left\lfloor\NVar{x}\right\rfloor$ : floor of $x$ , $\pi\left(\NVar{x}\right)$ : number of primes not exceeding a number, $p,p_{1},\ldots$ : prime numbers and $x$ : real number
Permalink:: http://dlmf.nist.gov/27.12.E3
Encodings:: pMML, png, TeX
See also:: Annotations for §27.12 and Ch.27

… ►The largest known prime (2018) is the Mersenne prime

2^{82,589,933}-1

. …

5: Bibliography I

… ►

IEEE (2018) IEEE Standard for Interval Arithmetic: IEEE Std 1788.1-2017. The Institute of Electrical and Electronics Engineers, Inc..

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External Links:: ISBN 978-1-5044-4602-0, Document
Referenced by:: §3.1(ii), §3.1(ii), Erratum (V1.0.25) for Section 3.1.
Encodings:: BibTeX

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Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi, and M. Harada (1993) The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of

J_{0}(z)-iJ_{1}(z)

and of Bessel functions

J_{m}(z)

of any real order

m

. Linear Algebra Appl. 194, pp. 35–70.

ⓘ

External Links:: ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt
Referenced by:: §10.21(ix).
Encodings:: BibTeX

…

6: 3.1 Arithmetics and Error Measures

… ►where

s

is equal to

1

0

, each

b_{j}

j\geq 1

, is either

0

1

b_{1}

is the most significant bit,

p

(

\in\mathbb{N}

) is the number of significant bits

b_{j}

b_{p-1}

is the least significant bit,

E

is an integer called the exponent,

b_{0}.b_{1}b_{2}\dots b_{p-1}

is the significand, and

f=.b_{1}b_{2}\dots b_{p-1}

is the fractional part. … ►with

b_{0}=1

and all allowable choices of

E

p

s

, and

b_{j}

. … ►Let

E_{{\rm min}}\leq E\leq E_{{\rm max}}

with

E_{{\rm min}}<0

and

E_{{\rm max}}>0

. … ►The respective machine precisions are

\frac{1}{2}\epsilon_{M}=0.596\times 10^{-7}

\frac{1}{2}\epsilon_{M}=0.111\times 10^{-15}

and

\frac{1}{2}\epsilon_{M}=0.963\times 10^{-34}

. … ►For interval arithmetic, one should refer to the IEEE Standards for Interval Arithmetic IEEE (2015, 2018). …

7: Bibliography O

… ►

K. Okamoto (1987c) Studies on the Painlevé equations. IV. Third Painlevé equation

P_{{\rm III}}

. Funkcial. Ekvac. 30 (2-3), pp. 305–332.

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External Links:: ISSN 0532-8721, FullText, MathReview (Hélène Airault), ZentralBlatt
Referenced by:: §32.10(iii), §32.2(iii), §32.6(iv), §32.7(viii).
Encodings:: BibTeX

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S. Olver (2011) Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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External Links:: ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §32.17, §32.17.
Encodings:: BibTeX

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M. Onoe (1956) Modified quotients of cylinder functions. Math. Tables Aids Comput. 10, pp. 27–28.

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External Links:: ISSN 0891-6837, MathReview Entry
Referenced by:: §10.29(i), §10.6(i).
Encodings:: BibTeX

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G. E. Ordóñez and D. J. Driebe (1996) Spectral decomposition of tent maps using symmetry considerations. J. Statist. Phys. 84 (1-2), pp. 269–276.

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External Links:: ISSN 0022-4715, Document, MathReview (Makoto Mori), ZentralBlatt
Referenced by:: §24.18.
Encodings:: BibTeX

… ►

H. Oser (1960) Algorithm 22: Riccati-Bessel functions of first and second kind. Comm. ACM 3 (11), pp. 600–601.

ⓘ

Notes:: Includes Algol code, minimum accuracy 9S. For certification see same journal 13(1970), p. 448.
External Links:: ISSN 0001-0782, Document
Referenced by:: §10.77(ii).
Encodings:: BibTeX

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