swallowtail%20canonical%20integral

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1: 36.4 Bifurcation Sets

… ► $K=1$, fold bifurcation set: … ► $K=3$, swallowtail bifurcation set: … ►Swallowtail self-intersection line: … ►Swallowtail cusp lines (ribs): … ►

§36.4(ii) Visualizations

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2: 36.5 Stokes Sets

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§36.5(ii) Cuspoids

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$K=3$. Swallowtail

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§36.5(iii) Umbilics

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§36.5(iv) Visualizations

… ►Red and blue numbers in each region correspond, respectively, to the numbers of real and complex critical points that contribute to the asymptotics of the canonical integral away from the bifurcation sets. …

3: Bibliography C

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

BibTeX

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A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives. Molecular Phys. 48 (6), pp. 1305–1330.

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External Links:

ISSN 0026-8976, Document, MathReview (Peter Giblin)

Referenced by:

§36.10(i), §36.10(ii), §36.15(v), §36.8.

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Evaluation of multidimensional canonical integrals in semiclassical collision theory. Molecular Phys. 26 (6), pp. 1371–1377.

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External Links:

Document

Referenced by:

§36.8.

Encodings:

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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External Links:

Document

Referenced by:

5th item.

Encodings:

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