int alle Customer 1-201-63O-76-80 Support Number int alle heine moll Free Number

(0.008 seconds)

1—10 of 274 matching pages

1: 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.

2: 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). …

3: 22.1 Special Notation

… ► ►►►►►►

$x, y$	real variables.
…
$k$	modulus. Except in §§22.3(iv), 22.17, and 22.19, $0\leq k\leq 1$ .
$k^{\prime}$	complementary modulus, $k^{2}+{k^{\prime}}^{2}=1$ . If $k\in[0,1]$ , then $k^{\prime}\in[0,1]$ .
$K$ , ${K^{\prime}}$	$K\left(k\right)$ , ${K^{\prime}}\left(k\right)=K\left(k^{\prime}\right)$ (complete elliptic integrals of the first kind (§19.2(ii))).
…
$\tau$	$i{K^{\prime}}/K$ .

►All derivatives are denoted by differentials, not primes. …

… ►, 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. …

5: 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. …

6: 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.

7: 19.1 Special Notation

… ►The first three functions are incomplete integrals of the first, second, and third kinds, and the

\operatorname{cel}

function includes complete integrals of all three kinds.

8: 27.21 Tables

§27.21 Tables

… ►Bressoud and Wagon (2000, pp. 103–104) supplies tables and graphs that compare

\pi\left(x\right),\ifrac{x}{\ln x}

, and

\operatorname{li}\left(x\right)

. … ►Lehmer (1941) gives a comprehensive account of tables in the theory of numbers, including virtually every table published from 1918 to 1941. … ►No sequel to Lehmer (1941) exists to date, but many tables of functions of number theory are included in Unpublished Mathematical Tables (1944).

9: 36.7 Zeros

… ►,

y=0

), the number of rings in the

m

th row, measured from the origin and before the transition to hairpins, is given by …

10: 19.25 Relations to Other Functions

… ►In (19.25.38) and (19.25.39)

j

k

\ell

is any permutation of the numbers

1,2,3

. ►

19.25.38

\omega_{j}=R_{F}\left(0,e_{j}-e_{k},e_{j}-e_{\ell}\right),

ⓘ

Symbols:: $R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)$ : symmetric elliptic integral of first kind, $e_{\NVar{j}}$ : Weierstrass lattice roots, $j$ : $(=1,2,3)$ , $z$ : complex number, $k$ : $(=1,2,3)$ , $\ell$ : $(=1,2,3)$ and $\omega_{j}$ : nonzero complex number
Proof sketch:: Take $z=-\omega$ in (19.25.35).
Referenced by:: §19.25(vi), §19.25(vi)
Permalink:: http://dlmf.nist.gov/19.25.E38
Encodings:: pMML, png, TeX
See also:: Annotations for §19.25(vi), §19.25 and Ch.19

►

19.25.39

\zeta\left(\omega_{j}\right)+\omega_{j}e_{j}=2R_{G}\left(0,e_{j}-e_{k},e_{j}-e% _{\ell}\right),

ⓘ

Symbols:: $R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)$ : symmetric elliptic integral of second kind, $e_{\NVar{j}}$ : Weierstrass lattice roots, $\zeta\left(\NVar{z}\right)$ (= $\zeta\left(z|\mathbb{L}\right)$ = $\zeta\left(z;g_{2},g_{3}\right)$ ): Weierstrass zeta function, $j$ : $(=1,2,3)$ , $z$ : complex number, $k$ : $(=1,2,3)$ , $\ell$ : $(=1,2,3)$ , $\omega_{j}$ : nonzero complex number and $\eta_{j}$ : complex number
Proof sketch:: Take $z=-\omega$ in (19.25.36).
Referenced by:: §19.25(vi), §19.25(vi), Erratum (V1.1.0) for Subsection 19.25(vi)
Permalink:: http://dlmf.nist.gov/19.25.E39
Encodings:: pMML, png, TeX
Correction (effective with 1.1.0):: This equation has been corrected such that the left-hand side $\eta_{j}$ has been replaced by $\zeta\left(\omega_{j}\right)$ .
See also:: Annotations for §19.25(vi), §19.25 and Ch.19

… ►

19.25.41

\sigma_{j}(z)=\exp\left(-\eta_{j}z\right)\ifrac{\sigma\left(z+\omega_{j}\right% )}{\sigma\left(\omega_{j}\right)},

j=1,2,3,

ⓘ

Defines:: $\sigma_{j}(z)$ : function (locally)
Symbols:: $\sigma\left(\NVar{z}\right)$ (= $\sigma\left(z|\mathbb{L}\right)$ = $\sigma\left(z;g_{2},g_{3}\right)$ ): Weierstrass sigma function, $\exp\NVar{z}$ : exponential function, $j$ : $(=1,2,3)$ , $z$ : complex number, $\omega_{j}$ : nonzero complex number and $\eta_{j}$ : complex number
Permalink:: http://dlmf.nist.gov/19.25.E41
Encodings:: pMML, png, TeX
See also:: Annotations for §19.25(vi), §19.25 and Ch.19

…