domain

SearchAdvancedHelp

(0.000 seconds)

1—10 of 47 matching pages

1: 37.20 Mathematical Applications

… ►OPs are essential for developing approximation theory on regular domains, including characterization of best approximation. … ►For regular domains, such as square, sphere, ball, simplex, and conic domains, they are used to study convolution structure, maximal functions, and interpolation spaces, as well as localized kernel and localized frames. … ►Although Gaussian cubature rules rarely exist and they do not exist for centrally symmetric domains, minimal or near minimal cubature rules on the unit square are known and provide efficient numerical integration rules. …

2: Possible Errors in DLMF

… ►One source of confusion, rather than actual errors, are some new functions which differ from those in Abramowitz and Stegun (1964) by scaling, shifts or constraints on the domain; see the Info box (click or hover over the icon) for links to defining formula. …

3: Bibliography Y

… ►

Generalized Hypergeometric Functions and Laguerre Polynomials in Two Variables. In Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemporary Mathematics, Vol. 138, pp. 239–259.

ⓘ

External Links:

MathReview (B. M. Agrawal), ZentralBlatt

Referenced by:

§35.10.

Encodings:

BibTeX

… ►

The calculation of the Riemann zeta function in the complex domain. USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

►

Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.

ⓘ

Notes:

Includes Fortran programs.

External Links:

Document, ZentralBlatt

Referenced by:

§25.18(i), §25.21(iii).

Encodings:

BibTeX

…

4: 14.26 Uniform Asymptotic Expansions

… ►The uniform asymptotic approximations given in §14.15 for $P_{\nu }^{-\mu }\left(x\right)$ and ${𝑸}_{\nu }^{\mu }\left(x\right)$ for are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). …

5: Donald St. P. Richards

… ►He is editor of the book Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, published by the American Mathematical Society in 1992, and coeditor of Representation Theory and Harmonic Analysis: A Conference in Honor of R. A. Kunze (with T. …

6: 37.18 Orthogonal Polynomials on Quadratic Domains

§37.18 Orthogonal Polynomials on Quadratic Domains

►These OPs are on the quadratic domain …Up to an affine transformation, this includes quadratic domains bounded by the quadratic surfaces in §37.12. … ►On the quadratic domain ${𝕍}^{d+1}$, define the inner product … ►

§37.18(ii) Jacobi Polynomials on the Cone

…

7: Bonita V. Saunders

… ►As the principal developer of graphics for the DLMF, she has collaborated with other NIST mathematicians, computer scientists, and student interns to produce informative graphs and dynamic interactive visualizations of elementary and higher mathematical functions over both simply and multiply connected domains. …

8: 1.10 Functions of a Complex Variable

… ►Let $f_1(z)$ be analytic in a domain $D_1$. … ►Let $F(z)$ be a multivalued function and $D$ be a domain. … ►A cut domain is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed. … … ►Suppose $D$ is a domain, and …

9: 1.9 Calculus of a Complex Variable

… ►When its boundary points are added the domain is said to be closed, but unless specified otherwise a domain is assumed to be open. … ► … ►

Jordan Curve Theorem

… ►One of these domains is bounded and is called the interior domain of $C$; the other is unbounded and is called the exterior domain of $C$. …

10: 1.13 Differential Equations

… ►

§1.13(i) Existence of Solutions

►A domain in the complex plane is simply-connected if it has no “holes”; more precisely, if its complement in the extended plane $ℂ\cup \{\mathrm{\infty }\}$ is connected. … ►where $z\in D$, a simply-connected domain, and $f(z)$, $g(z)$ are analytic in $D$, has an infinite number of analytic solutions in $D$. … ► $u$ and $z$ belong to domains $U$ and $D$ respectively, the coefficients $f(u,z)$ and $g(u,z)$ are continuous functions of both variables, and for each fixed $u$ (fixed $z$) the two functions are analytic in $z$ (in $u$). … ►with $f(z)$, $g(z)$, and $r(z)$ analytic in $D$ has infinitely many analytic solutions in $D$. …