poristic polygon constructions of Poncelet

SearchAdvancedHelp

(0.003 seconds)

1—10 of 67 matching pages

1: 22.8 Addition Theorems

… ►Greenhill (1959, pp. 121–130) reviews these results in terms of the geometric poristic polygon constructions of Poncelet. …

2: Bibliography H

… ►

Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.

ⓘ

Notes:

Reprinted in 1993.

External Links:

ISBN 0-471-08703-3; 0-471-58986-1, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.14(v), Ch.3.

Encodings:

BibTeX

… ►

Poncelet Polygons and the Painlevé Equations. In Geometry and Analysis (Bombay, 1992), Ramanan (Ed.), pp. 151–185.

ⓘ

External Links:

MathReview (Henrik Pedersen), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX

…

3: Bibliography G

… ►

Construction of Gauss-Christoffel quadrature formulas. Math. Comp. 22, pp. 251–270.

ⓘ

External Links:

ISSN 0025-5718, Document, Link, MathReview (R. E. Barnhill)

Referenced by:

§18.39(iii).

Encodings:

BibTeX

… ►

New method for constructing wavefunctions for bound states and scattering. J. Chem. Phys. 51, pp. 14–25.

ⓘ

External Links:

Document, MathReview (K. J. Le Couteur)

Referenced by:

§9.11(iv), §9.17(iii).

Encodings:

BibTeX

►

Constructing wavefunctions for nonlocal potentials. J. Chem. Phys. 52, pp. 6211–6217.

ⓘ

External Links:

Document, MathReview (D. B. Fairlie)

Referenced by:

(9.12.22), (9.12.23), §9.12(vii), §9.17(iii).

Encodings:

BibTeX

… ►

Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions. Phys. Rev. E 47 (4), pp. R2233–R2236.

ⓘ

External Links:

Document

Referenced by:

§19.35(ii).

Encodings:

BibTeX

4: 9.15 Mathematical Applications

… ►Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point. …

5: 27.17 Other Applications

… ►Congruences are used in constructing perpetual calendars, splicing telephone cables, scheduling round-robin tournaments, devising systematic methods for storing computer files, and generating pseudorandom numbers. …Apostol and Zuckerman (1951) uses congruences to construct magic squares. …

6: Joyce E. Conlon

… ►In 1999 she joined the NIST Mathematical and Computational Sciences Division, where she contributed to the DLMF project, especially in the construction of the bibliography. …

7: Tom H. Koornwinder

… ►Currently he is on the editorial board for Constructive Approximation, and is editor for the volume on Multivariable Special Functions in the ongoing Askey–Bateman book project. …

8: Bruce R. Miller

… ►In particular, he developed the LaTeXML system used for converting the LaTeX source documents into XML and MathML from which the DLMF website is constructed. …

9: Peter L. Walker

… ►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …

10: 10.72 Mathematical Applications

… ►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter. … ►In regions in which (10.72.1) has a simple turning point $z_0$, that is, $f(z)$ and $g(z)$ are analytic (or with weaker conditions if $z=x$ is a real variable) and $z_0$ is a simple zero of $f(z)$, asymptotic expansions of the solutions $w$ for large $u$ can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order $\frac{1}{3}$ (§9.6(i)). … ►If $f(z)$ has a double zero $z_0$, or more generally $z_0$ is a zero of order $m$, $m=2,3,4,\mathrm{\dots }$, then uniform asymptotic approximations (but not expansions) can be constructed in terms of Bessel functions, or modified Bessel functions, of order $1/(m+2)$. … ►In regions in which the function $f(z)$ has a simple pole at $z=z_0$ and ${(z-z_0)}^{2}g(z)$ is analytic at $z=z_0$ (the case $\lambda =-1$ in §10.72(i)), asymptotic expansions of the solutions $w$ of (10.72.1) for large $u$ can be constructed in terms of Bessel functions and modified Bessel functions of order $\pm \sqrt{1+4\rho }$, where $\rho$ is the limiting value of ${(z-z_0)}^{2}g(z)$ as $z\to z_0$. … ►Then for large $u$ asymptotic approximations of the solutions $w$ can be constructed in terms of Bessel functions, or modified Bessel functions, of variable order (in fact the order depends on $u$ and $\alpha$). …