analytic properties

SearchAdvancedHelp

(0.002 seconds)

11—20 of 72 matching pages

11: 33.2 Definitions and Basic Properties

… ►

§33.2(i) Coulomb Wave Equation

… ►

§33.2(ii) Regular Solution $F_{\mathrm{\ell }}(\eta ,\rho )$

… ►

§33.2(iii) Irregular Solutions $G_{\mathrm{\ell }}(\eta ,\rho ),H_{\mathrm{\ell }}^{\pm }(\eta ,\rho )$

…

12: 33.14 Definitions and Basic Properties

… ►

§33.14(i) Coulomb Wave Equation

… ►

§33.14(ii) Regular Solution $f(ϵ,\mathrm{\ell };r)$

… ►

§33.14(iii) Irregular Solution $h(ϵ,\mathrm{\ell };r)$

…

13: 14.21 Definitions and Basic Properties

… ► …

14: 25.15 Dirichlet $L$-functions

… ►

§25.15(i) Definitions and Basic Properties

…

15: 23.15 Definitions

… ► …

16: 25.12 Polylogarithms

… ►

§25.12(i) Dilogarithms

… ►

§25.12(ii) Polylogarithms

…

17: 28.12 Definitions and Basic Properties

… ►

§28.12(iii) Functions ${\mathrm{ce}}_{\nu }(z,q)$, ${\mathrm{se}}_{\nu }(z,q)$, when $\nu \notin \mathbb{Z}$

…

18: 25.2 Definition and Expansions

§25.2 Definition and Expansions

…

19: 21.2 Definitions

… ►

21.2.1 $$\theta \left(𝐳\right|𝛀)=\sum _{𝐧\in {\mathbb{Z}}^g}{\mathrm{e}}^{2\pi \mathrm{i}\left(\frac{1}{2}𝐧\cdot 𝛀\cdot 𝐧+𝐧\cdot 𝐳\right)}.$$

ⓘ

Defines:

$\theta \left(𝐳\right|𝛀)$: Riemann theta function

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $\in$: element of, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\mathbb{Z}$: set of all integers, $g$: positive integer and $𝛀$: a Riemann matrix

Referenced by:

§21.2(ii)

Permalink:

http://dlmf.nist.gov/21.2.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §21.2(i), §21.2 and Ch.21

…

20: 16.5 Integral Representations and Integrals

… ►where the contour of integration separates the poles of $\mathrm{\Gamma }\left(a_k+s\right)$, $k=1,\mathrm{\dots },p$, from those of $\mathrm{\Gamma }\left(-s\right)$. …