with respect to amplitude

SearchAdvancedHelp

(0.003 seconds)

11—14 of 14 matching pages

11: 29.1 Special Notation

… ► ►►►

$m,n,p$	nonnegative integers.
…
$K$, $K^{\prime }$	complete elliptic integrals of the first kind with moduli $k,k^{\prime }$, respectively (see §19.2(ii)).

… ►The notation for the eigenvalues and functions is due to Erdélyi et al. (1955, §15.5.1) and that for the polynomials is due to Arscott (1964b, §9.3.2). … ►The relation to the Lamé functions $L_{c\nu }^{(m)}$, $L_{s\nu }^{(m)}$of Jansen (1977) is given by …where $\psi =\mathrm{am}(z,k)$; see §22.16(i). The relation to the Lamé functions ${\mathrm{Ec}}_{\nu }^m$, ${\mathrm{Es}}_{\nu }^m$ of Ince (1940b) is given by …

12: 28.33 Physical Applications

… ►We shall derive solutions to the uniform, homogeneous, loss-free, and stretched elliptical ring membrane with mass $\rho$ per unit area, and radial tension $\tau$ per unit arc length. … ►For a visualization see Gutiérrez-Vega et al. (2003), and for references to other boundary-value problems see: … ►As $\omega$ runs from $0$ to $+\mathrm{\infty }$, with $b$ and $f$ fixed, the point $(q,a)$ moves from $\mathrm{\infty }$ to $0$ along the ray $ℒ$ given by the part of the line $a=(2b/f)q$ that lies in the first quadrant of the $(q,a)$-plane. … ►However, in response to a small perturbation at least one solution may become unbounded. … ►

McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

…

13: Bibliography B

… ►

An Introduction to Linear Difference Equations. Dover Publications Inc., New York.

ⓘ

Notes:

Unaltered republication of the original 1927 Harvard University edition.

External Links:

MathReview, ZentralBlatt

Referenced by:

§8.1, Notations P, Notations Q.

Encodings:

BibTeX

… ►

The fifty-two icosahedral solutions to Painlevé VI. J. Reine Angew. Math. 596, pp. 183–214.

ⓘ

External Links:

ISSN 0075-4102, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX

… ►

On the derivatives of the Bessel and Struve functions with respect to the order. Integral Transforms Spec. Funct. 16 (3), pp. 187–198.

ⓘ

External Links:

ISSN 1065-2469, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.15, §10.38, §11.4(vi).

Encodings:

BibTeX

… ►

The determination of phases and amplitudes of wave functions. Proc. Phys. Soc. 81 (3), pp. 442–452.

ⓘ

External Links:

Document

Referenced by:

§33.23(vii).

Encodings:

BibTeX

… ►

A Guide to Mathematical Tables: Supplement No. 1. Pergamon Press, New York.

ⓘ

Notes:

Supplement to “A Guide to Mathematical Tables” by A. V. Lebedev and R. M. Fedorova.

External Links:

MathReview

Referenced by:

A. V. Lebedev and R. M. Fedorova (1960).

Encodings:

BibTeX

…

14: Bibliography C

… ►

Introduction to the Theory of Fourier’s Series and Integrals. 3rd edition, Macmillan, London.

ⓘ

Notes:

Reprinted by Dover, New York, 1950.

External Links:

ZentralBlatt

Referenced by:

§6.16(i).

Encodings:

BibTeX

… ►

Introduction to Approximation Theory. 2nd edition, Chelsea Publishing Co., New York.

ⓘ

Notes:

Reprinted by AMS Chelsea Publishing, Providence, RI, 1998

External Links:

ISBN 0-8218-1374-9, MathReview, ZentralBlatt

Referenced by:

§18.38(i).

Encodings:

BibTeX

… ►

Derivatives with respect to the degree and order of associated Legendre functions for $|z|>1$ using modified Bessel functions. Integral Transforms Spec. Funct. 21 (7-8), pp. 581–588.

ⓘ

External Links:

ISSN 1065-2469, Document, FullText, MathReview (Dmitriy Karp), ZentralBlatt

Referenced by:

§14.11, §14.11.

Encodings:

BibTeX

… ►

Constraints on the phase of scattering amplitudes due to positivity. Nuclear Phys. B 49, pp. 413–440.

ⓘ

External Links:

Document

Referenced by:

§18.39(v).

Encodings:

BibTeX

►

Constraints on the phases of helicity amplitudes due to positivity. Nuclear Phys. B 77, pp. 141–162.

ⓘ

External Links:

Document, MathReview

Referenced by:

§18.39(v).

Encodings:

BibTeX

…