discontinuity

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11—19 of 19 matching pages

11: 4.37 Inverse Hyperbolic Functions

…

12: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►Often circumstances allow rather stronger statements, such as uniform convergence, or pointwise convergence at points where

f(x)

is continuous, with convergence to

(f(x_{0}-)+f(x_{0}+))/2

x_{0}

is an isolated point of discontinuity. … ►This is the discontinuity across the branch cut in (1.18.52)

\boldsymbol{\sigma}_{c}\subset\mathbb{R}

, from

z

below to above the cut, divided by

2\pi\mathrm{i}

. … ►This representation has poles with residues

{\left|\widehat{f}(\lambda_{n})\right|}^{2}

at the discrete eigenvalues and a branch cut along

[0,\infty)

with discontinuity, from below to above the cut,

2\pi\mathrm{i}{\left|\widehat{f}(\lambda)\right|}^{2}

, as in (1.18.53), see Newton (2002, §7.1.1). …

13: Bibliography B

… ►

M. V. Berry (1989) Uniform asymptotic smoothing of Stokes’s discontinuities. Proc. Roy. Soc. London Ser. A 422, pp. 7–21.

ⓘ

External Links:: ISSN 0080-4630, FullText, MathReview (André Hautot), ZentralBlatt
Referenced by:: §2.11(iv).
Encodings:: BibTeX

…

14: Bibliography S

… ►

R. Sips (1970) Quelques intégrales définies discontinues contenant des fonctions de Mathieu. Acad. Roy. Belg. Bull. Cl. Sci. (5) 56 (5), pp. 475–491 (French).

ⓘ

External Links:: MathReview (F. M. Arscott), ZentralBlatt
Referenced by:: §28.28(i), §28.28(v).
Encodings:: BibTeX

…

15: 10.22 Integrals

… ►

Weber–Schafheitlin Discontinuous Integrals, including Special Cases

…

16: 2.11 Remainder Terms; Stokes Phenomenon

… ►That the change in their forms is discontinuous, even though the function being approximated is analytic, is an example of the Stokes phenomenon. …