Stokes%20multipliers

SearchAdvancedHelp

(0.003 seconds)

1—10 of 129 matching pages

1: 36.5 Stokes Sets

§36.5 Stokes Sets

►

§36.5(i) Definitions

… ►

§36.5(ii) Cuspoids

… ►

Elliptic Umbilic Stokes Set (Codimension three)

… ►

§36.5(iv) Visualizations

…

2: 2.11 Remainder Terms; Stokes Phenomenon

§2.11 Remainder Terms; Stokes Phenomenon

… ►

§2.11(iv) 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. Where should the change-over take place? Can it be accomplished smoothly? … ►For higher-order Stokes phenomena see Olde Daalhuis (2004b) and Howls et al. (2004). …

3: Bibliography O

… ►

On the calculation of Stokes multipliers for linear differential equations of the second order. Methods Appl. Anal. 2 (3), pp. 348–367.

ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

… ►

On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation. J. Comput. Appl. Math. 169 (1), pp. 235–246.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Jorge Mozo Fernández), ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX

… ►

An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

ⓘ

External Links:

Document, MathReview (David L. Elliott), ZentralBlatt

Referenced by:

§3.11(ii).

Encodings:

BibTeX

…

4: Bibliography P

… ►

Stokes phenomenon demystified. Bull. Inst. Math. Appl. 31 (1-2), pp. 21–28.

ⓘ

External Links:

ISSN 0905-5628, MathReview Entry, ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX

… ►

Smoothing of the Stokes phenomenon for high-order differential equations. Proc. Roy. Soc. London Ser. A 436, pp. 165–186.

ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

►

Smoothing of the Stokes phenomenon using Mellin-Barnes integrals. J. Comput. Appl. Math. 41 (1-2), pp. 117–133.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Anatoly Kilbas), ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

… ►

The Stokes phenomenon associated with the Hurwitz zeta function $\zeta (s,a)$ . Proc. Roy. Soc. London Ser. A 461, pp. 297–304.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview (Marc Prevost), ZentralBlatt

Referenced by:

(25.11.43), §25.11(xii).

Encodings:

BibTeX

… ►

Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

…

5: 2.7 Differential Equations

… ►

$w_2(z)={\mathrm{e}}^{-2\pi \mathrm{i}{\mu }_2}{w}_2(z{\mathrm{e}}^{2\pi \mathrm{i}})+C_2{w}_1(z),$

►in which $C_1$, $C_2$ are constants, the so-called Stokes multipliers. … ►For the calculation of Stokes multipliers see Olde Daalhuis and Olver (1995b). …

6: Bibliography I

… ►

The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX

… ►

Quasi-linear Stokes phenomenon for the second Painlevé transcendent. Nonlinearity 16 (1), pp. 363–386.

ⓘ

External Links:

ISSN 0951-7715, Document, MathReview (Youmin Lu), ZentralBlatt

Referenced by:

§32.12(ii).

Encodings:

BibTeX

…

7: Bibliography W

… ►

The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

BibTeX

… ►

Smoothing of Stokes’s discontinuity for the generalized Bessel function. II. Proc. Roy. Soc. London Ser. A 455, pp. 3065–3084.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§10.46.

Encodings:

BibTeX

►

Smoothing of Stokes’s discontinuity for the generalized Bessel function. Proc. Roy. Soc. London Ser. A 455, pp. 1381–1400.

ⓘ

External Links:

ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§10.46.

Encodings:

BibTeX

… ►

The Stokes set of the cusp diffraction catastrophe. J. Phys. A 13 (9), pp. 2913–2928.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview (I. Stewart), ZentralBlatt

Referenced by:

§36.5(ii).

Encodings:

BibTeX

…

8: Bibliography B

… ►

Stokes surfaces of diffraction catastrophes with codimension three. Nonlinearity 3 (2), pp. 281–291.

ⓘ

External Links:

ISSN 0951-7715, Document, MathReview (Maria Carmen Romero-Fuster), ZentralBlatt

Referenced by:

§36.2(i), §36.5(ii), §36.5(iii), §36.5(iv).

Encodings:

BibTeX

… ►

Overlapping Stokes smoothings: Survival of the error function and canonical catastrophe integrals. Proc. Roy. Soc. London Ser. A 444, pp. 201–216.

ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX

… ►

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

►

Infinitely many Stokes smoothings in the gamma function. Proc. Roy. Soc. London Ser. A 434, pp. 465–472.

ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§5.11(ii).

Encodings:

BibTeX

… ►

Stieltjes transforms and the Stokes phenomenon. Proc. Roy. Soc. London Ser. A 429, pp. 227–246.

ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

…

9: 7.20 Mathematical Applications

… ►For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951). ►The complementary error function also plays a ubiquitous role in constructing exponentially-improved asymptotic expansions and providing a smooth interpretation of the Stokes phenomenon; see §§2.11(iii) and 2.11(iv). …

10: Bibliography K

… ►

Essential singularity of the Painlevé function of the second kind and the nonlinear Stokes phenomenon. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 187, pp. 139–170 (Russian).

ⓘ

Notes:

English translation: J. Math. Sci. 73(1995), no. 4, pp. 500–517

External Links:

ISSN 0373-2703, Document, MathReview (Andreĭ Bolibrukh), ZentralBlatt

Referenced by:

§32.12(ii).

Encodings:

BibTeX

►

Quasi-linear Stokes phenomenon for the Painlevé first equation. J. Phys. A 37 (46), pp. 11149–11167.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§32.12(i).

Encodings:

BibTeX

… ►

Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

ⓘ

External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

… ►

Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

ⓘ

External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

…