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1: 24.1 Special Notation

… ►

Bernoulli Numbers and Polynomials

►The origin of the notation

B_{n}

B_{n}\left(x\right)

, is not clear. … ►

Euler Numbers and Polynomials

… ►Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations

E_{n}

E_{n}\left(x\right)

, as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …

2: Customize DLMF

Customize DLMF

You can customize the appearance and functionality of the DLMF site using these selections. Note: Javascript and Cookies must be enabled to support customizations.

… ►, built-in to the browser) support for MathML is growing, (see Browsers supporting MathML). …By default, DLMF will use Native support when available; You may choose how MathML is processed (Native or MathJax) at Customize DLMF. ►In rare cases, a browser lacks both MathML support and a robust enough javascript implementation capable of running MathJax; you may wish to visit the Customize DLMF page and choose the HTML+images document format. … ►

Browsers supporting MathML

… ►Recent enhancements to the WebKit engine now provide support for MathML Core. …

4: Browsers

… ►Most modern browsers support either MathML, or the MathJax fallback acceptably; If yours does not, please consider upgrading. …If none of those solutions work for you, you may explicitly choose a format such as HTML+images, using images for mathematics, at Customize DLMF. …

5: Viewing DLMF Interactive 3D Graphics

… ►WebGL is supported in the current versions of most common web browsers. … ►1, some advanced features of X3DOM are currently not fully supported (see x3dom.org). …If you have trouble viewing the WebGL visualizations in your web browser, see x3dom.org or caniuse.com/webgl for information on WebGL browser support. … ►After installing the viewer you must select Customize DLMF on the DLMF Menu bar and choose either VRML or X3D under “Visualization Format. … ►Please see caniuse.com/webgl or x3dom.org for information on WebGL browser support.

6: DLMF Project News

error generating summary

7: Guide to Searching the DLMF

… ►

term:

a textual word, a number, or a math symbol.

►

phrase:

any double-quoted sequence of textual words and numbers.

… ►

proximity operator:

adj, prec/n, and near/n, where n is any positive natural number.

… ►Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect. … ►For example, you may want equations that contain trigonometric functions, but you don’t care which trigonometric function. …

8: Preface

… ►Lozier directed the NIST research, technical, and support staff associated with the project, administered grants and contracts, together with Boisvert compiled the Software sections for the Web version of the chapters, conducted editorial and staff meetings, represented the project within NIST and at professional meetings in the United States and abroad, and together with Olver carried out the day-to-day development of the project. … ►All of the mathematical information contained in the Handbook is also contained in the DLMF, along with additional features such as more graphics, expanded tables, and higher members of some families of formulas; in consequence, in the Handbook there are occasional gaps in the numbering sequences of equations, tables, and figures. … ►Among the research, technical, and support staff at NIST these are B. … ►Notwithstanding the great care that has been exercised by the editors, authors, validators, and the NIST staff, it is almost inevitable that in a work of the magnitude and scope of the NIST Handbook and DLMF errors will still be present. …

9: 26.11 Integer Partitions: Compositions

… ►

c\left(n\right)

denotes the number of compositions of

n

, and

c_{m}\left(n\right)

is the number of compositions into exactly

m

parts.

c\left(\in\!T,n\right)

is the number of compositions of

n

with no 1’s, where again

T=\{2,3,4,\ldots\}

. … ►

26.11.1

c\left(0\right)=c\left(\in\!T,0\right)=1.

ⓘ

Symbols:: $\in$ : element of, $c\left(\NVar{n}\right)$ : number of compositions of $n$ , $c\left(\NVar{\mathrm{condition}},\NVar{n}\right)$ : restricted number of compositions of $n$ and $T$ : set
Permalink:: http://dlmf.nist.gov/26.11.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §26.11 and Ch.26

… ►The Fibonacci numbers are determined recursively by … ►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).

10: 27.18 Methods of Computation: Primes

§27.18 Methods of Computation: Primes

►An overview of methods for precise counting of the number of primes not exceeding an arbitrary integer

x

is given in Crandall and Pomerance (2005, §3.7). …An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000). … ►These algorithms are used for testing primality of Mersenne numbers,

2^{n}-1

, and Fermat numbers,

2^{2^{n}}+1

. …