Bleistein method

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1: 2.3 Integrals of a Real Variable

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§2.3(v) Coalescing Peak and Endpoint: Bleistein’s Method

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2: Bibliography K

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Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.

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External Links:

ISSN 1364-5021, Document, FullText, MathReview (Ulrich D. Jentschura), ZentralBlatt

Referenced by:

§2.4(vi), §2.4(vi).

Encodings:

BibTeX

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3: 2.4 Contour Integrals

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§2.4(iii) Laplace’s Method

… ►For this reason the name method of steepest descents is often used. … ►The last reference also includes examples, as do Olver (1997b, Chapter 4), Wong (1989, Chapter 2), and Bleistein and Handelsman (1975, Chapter 7). ►

§2.4(v) Coalescing Saddle Points: Chester, Friedman, and Ursell’s Method

… ►For examples, proofs, and extensions see Olver (1997b, Chapter 9), Wong (1989, Chapter 7), Olde Daalhuis and Temme (1994), Chester et al. (1957), Bleistein and Handelsman (1975, Chapter 9), and Temme (2015). …

4: 2.5 Mellin Transform Methods

… ►For further discussion of this method and examples, see Wong (1989, Chapter 3), Paris and Kaminski (2001, Chapter 5), and Bleistein and Handelsman (1975, Chapters 4 and 6). …

5: Bibliography B

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Asymptotic methods in enumeration. SIAM Rev. 16 (4), pp. 485–515.

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External Links:

Document, MathReview (Bernard Harris), ZentralBlatt

Referenced by:

Ch.2.

Encodings:

BibTeX

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Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt

Referenced by:

§3.11(v).

Encodings:

BibTeX

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Asymptotic Expansions of Integrals. Holt, Rinehart, and Winston, New York.

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Notes:

Reprinted with corrections by Dover Publications Inc., New York, 1986

External Links:

ISBN 0-486-65082-0, MathReview, ZentralBlatt

Referenced by:

§2.3(ii), §2.3(v), §2.4(iv), §2.4(v), §2.5(iii), §2.5(ii), Ch.2, Ch.9.

Encodings:

BibTeX

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Uniform asymptotic expansions of integrals with stationary point near algebraic singularity. Comm. Pure Appl. Math. 19, pp. 353–370.

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External Links:

Document, MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§2.3(v).

Encodings:

BibTeX

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Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities. J. Math. Mech. 17, pp. 533–559.

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX

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