”lecain” Customer service Number 1206⤄360⤄1604 contact ☎️"Number"

(0.004 seconds)

1—10 of 237 matching pages

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.

4: Bibliography L

… ►

J. LeCaine (1945) A table of integrals involving the functions

E_{n}(x)

ⓘ

Notes:: National Research Council of Canada, Division of Atomic Energy, Document no. MT-131 (NRC 1553)
Referenced by:: §8.19(x).
Encodings:: BibTeX

… ►

D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

ⓘ

External Links:: MathReview (D. H. Lehmer), ZentralBlatt
Referenced by:: §24.11.
Encodings:: BibTeX

… ►

D. H. Lehmer (1941) Guide to Tables in the Theory of Numbers. Bulletin of the National Research Council, No. 105, National Research Council, Washington, D.C..

ⓘ

Notes:: Reprinted in 1961.
External Links:: MathReview (R. D. Carmichael), ZentralBlatt
Referenced by:: §27.20, §27.20, §27.21, §27.21.
Encodings:: BibTeX

►

D. N. Lehmer (1914) List of Prime Numbers from 1 to 10,006,721. Publ. No. 165, Carnegie Institution of Washington, Washington, D.C..

ⓘ

External Links:: ZentralBlatt
Referenced by:: §27.21.
Encodings:: BibTeX

… ►

D. W. Lozier (1980) Numerical Solution of Linear Difference Equations. NBSIR Technical Report 80-1976, National Bureau of Standards, Gaithersburg, MD 20899.

ⓘ

Notes:: (Available from National Technical Information Service, Springfield, VA 22161.)
Referenced by:: §16.25, §3.6(vii).
Encodings:: BibTeX

…

… ►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. …

6: 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. …

7: 8.19 Generalized Exponential Integral

… ►For

j=1,2,3,\dots

, ►

8.19.15

\frac{{\partial}^{j}E_{p}\left(z\right)}{{\partial p}^{j}}=(-1)^{j}\int_{1}^{% \infty}(\ln t)^{j}t^{-p}e^{-zt}\,\mathrm{d}t,

\Re z>0

ⓘ

Symbols:: $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $\mathrm{e}$ : base of natural logarithm, $E_{\NVar{p}}\left(\NVar{z}\right)$ : generalized exponential integral, $\int$ : integral, $\ln\NVar{z}$ : principal branch of logarithm function, $\frac{\partial\NVar{f}}{\partial\NVar{x}}$ : partial derivative of $f$ with respect to $x$ , $\,\partial\NVar{x}$ : partial differential of $x$ , $\Re$ : 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). …

8: 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. …

9: Notices

… ►These software indexes are provided as a service to the user community. NIST expressly does not endorse or recommend any specific product or service. …Please contact us if you have software that you believe should be listed.

10: Ronald F. Boisvert

… ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. … ►Department of Commerce Gold Medal for Distinguished Achievement in the Federal Service in 2011, and an Outstanding Alumni Award from the Purdue University Department of Computer Science in 2012. …