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1: 24.1 Special Notation

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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

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3: About 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. …

4: Browsers

… ►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

… ►After installing the viewer you must select Customize DLMF on the DLMF Menu bar and choose either VRML or X3D under “Visualization Format. …

6: Bibliography L

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A table of integrals involving the functions $E_n(x)$ .

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Notes:

National Research Council of Canada, Division of Atomic Energy, Document no. MT-131 (NRC 1553)

Referenced by:

§8.19(x).

Encodings:

BibTeX

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

Encodings:

BibTeX

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Guide to Tables in the Theory of Numbers. Bulletin of the National Research Council, No. 105, National Research Council, Washington, D.C..

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Notes:

Reprinted in 1961.

External Links:

MathReview (R. D. Carmichael), ZentralBlatt

Referenced by:

§27.20, §27.20, §27.21, §27.21.

Encodings:

BibTeX

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List of Prime Numbers from 1 to 10,006,721. Publ. No. 165, Carnegie Institution of Washington, Washington, D.C..

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External Links:

ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX

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Highly accurate tables for elementary functions. BIT 35 (3), pp. 352–360.

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External Links:

ISSN 0006-3835, Document, MathReview, ZentralBlatt

Referenced by:

§4.45(i), §4.46.

Encodings:

BibTeX

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7: DLMF Project News

error generating summary

8: 8.19 Generalized Exponential Integral

… ►For $j=1,2,3,\mathrm{\dots }$, ►

8.19.15 $$\frac{{\partial }^j{E}_p\left(z\right)}{{\partial p}^j}={(-1)}^j{\int }_1^{\mathrm{\infty }}{(\ln t)}^j{t}^{-p}{\mathrm{e}}^{-zt}dt,$$ $\mathrm{\Re }z>0$.

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Symbols:

$dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $E_p\left(z\right)$: generalized exponential integral, $\int$: integral, $\ln z$: principal branch of logarithm function, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $\mathrm{\Re }$: real part, $z$: complex variable, $p$: parameter and $j$: numbers

Permalink:

http://dlmf.nist.gov/8.19.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §8.19(v), §8.19(v), §8.19 and Ch.8

… ►For collections of integrals involving $E_p\left(z\right)$, especially for integer $p$, see Apelblat (1983, §§7.1–7.2) and LeCaine (1945). …

9: Guide to Searching the DLMF

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

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any double-quoted sequence of textual words and numbers.

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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. …

10: 31.18 Methods of Computation

… ►Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)). …