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11: 2.7 Differential Equations

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

►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). …

12: Bibliography B

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

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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:

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

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External Links:

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

Referenced by:

§36.12(iii).

Encodings:

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Uniform asymptotic smoothing of Stokes’s discontinuities. Proc. Roy. Soc. London Ser. A 422, pp. 7–21.

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External Links:

ISSN 0080-4630, FullText, MathReview (André Hautot), ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX

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

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External Links:

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

Referenced by:

§5.11(ii).

Encodings:

BibTeX

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

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External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

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13: 1.6 Vectors and Vector-Valued Functions

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Stokes’s Theorem

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14: 6.12 Asymptotic Expansions

… ►For re-expansions of the remainder term leading to larger sectors of validity, exponential improvement, and a smooth interpretation of the Stokes phenomenon, see §§2.11(ii)–2.11(iv), with $p=1$. …

15: Bibliography K

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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).

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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:

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

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External Links:

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

Referenced by:

§32.12(i).

Encodings:

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16: Bibliography H

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On the higher-order Stokes phenomenon. Proc. Roy. Soc. London Ser. A 460, pp. 2285–2303.

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External Links:

ISSN 1364-5021, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX

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17: 3.10 Continued Fractions

… ►A more stable version of the algorithm is discussed in Stokes (1980). …

18: Bibliography D

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Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.

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External Links:

ISSN 0962-8444, FullText, MathReview (Alexander Tovbis), ZentralBlatt

Referenced by:

§2.11(iii), §8.20(ii).

Encodings:

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19: Bibliography S

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A stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§3.10(ii).

Encodings:

BibTeX

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