method of steepest descents

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1: Bibliography B

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Error bounds for the method of steepest descents. Proc. Roy. Soc. London Ser. A 440, pp. 493–518.

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External Links:

ISSN 0962-8444, FullText, MathReview (Pablo Martín), ZentralBlatt

Referenced by:

§2.3(iii), §2.4(iii), §9.10(ii).

Encodings:

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Gamma function asymptotics by an extension of the method of steepest descents. Proc. Roy. Soc. London Ser. A 447, pp. 609–630.

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External Links:

ISSN 0962-8444, FullText, MathReview (Jens Bolte), ZentralBlatt

Referenced by:

§5.11(i), §5.11(ii), §5.11(ii), (5.9.11_1), (5.9.11_2).

Encodings:

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Approximations for the late coefficients in asymptotic expansions arising in the method of steepest descents. Methods Appl. Anal. 2 (4), pp. 475–489.

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External Links:

ISSN 1073-2772, Pdf, MathReview (Dan Polis̆evski), ZentralBlatt

Referenced by:

§2.4(iv).

Encodings:

BibTeX

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2: 2.4 Contour Integrals

… ►Paths on which $\mathrm{\Im }\left(zp(t)\right)$ is constant are also the ones on which $|\exp \left(-zp(t)\right)|$ decreases most rapidly. For this reason the name method of steepest descents is often used. …

3: Bibliography P

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Exactification of the method of steepest descents: The Bessel functions of large order and argument. Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.

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External Links:

ISSN 1364-5021, Document, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§10.20(ii).

Encodings:

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4: 13.20 Uniform Asymptotic Approximations for Large $\mu$

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5: Bibliography C

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An extension of the method of steepest descents. Proc. Cambridge Philos. Soc. 53, pp. 599–611.

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External Links:

MathReview (P. Henrici), ZentralBlatt

Referenced by:

§2.4(v).

Encodings:

BibTeX

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6: 9.17 Methods of Computation

… ►In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent (§2.4(iv)). …

7: Bibliography T

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Steepest descent paths for integrals defining the modified Bessel functions of imaginary order. Methods Appl. Anal. 1 (1), pp. 14–24.

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External Links:

ISSN 1073-2772, FullText, MathReview (Anatoly Kilbas), ZentralBlatt

Referenced by:

§10.74(viii).

Encodings:

BibTeX

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8: 3.5 Quadrature

… ►Stroud and Secrest (1966) includes computational methods and extensive tables. … ►

§3.5(ix) Other Contour Integrals

… ►For example, steepest descent paths can be used; see §2.4(iv). … ►The steepest descent path is given by $\mathrm{\Im }\left(t-2\sqrt{t}\right)=0$, or in polar coordinates $t=r{\mathrm{e}}^{\mathrm{i}\theta }$ we have $r={\sec }^2\left(\frac{1}{2}\theta \right)$. … ►A special case is the rule for Hilbert transforms (§1.14(v)): …

9: 5.21 Methods of Computation

§5.21 Methods of Computation

… ►Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …