elliptic umbilic canonical integral

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11: 36.5 Stokes Sets

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§36.5(iii) Umbilics

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Figure 36.5.8: Sheets of the Stokes surface for the elliptic umbilic catastrophe (colored and with mesh) and the bifurcation set (gray). Magnify

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12: 36.12 Uniform Approximation of Integrals

… ►For further information concerning integrals with several coalescing saddle points see Arnol’d et al. (1988), Berry and Howls (1993, 1994), Bleistein (1967), Duistermaat (1974), Ludwig (1966), Olde Daalhuis (2000), and Ursell (1972, 1980).

13: 36.4 Bifurcation Sets

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Critical Points for Umbilics

… ► $K=1$, fold bifurcation set: … ►Elliptic umbilic bifurcation set (codimension three): for fixed $z$, the section of the bifurcation set is a three-cusped astroid … ►Elliptic umbilic cusp lines (ribs): … ►

§36.4(ii) Visualizations

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14: Bibliography B

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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:

BibTeX

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The elliptic umbilic diffraction catastrophe. Phil. Trans. Roy. Soc. Ser. A 291 (1382), pp. 453–484.

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External Links:

FullText

Referenced by:

§36.15(iv), §36.2(i), §36.7(ii), §36.7(iii).

Encodings:

BibTeX

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Numerical calculation of elliptic integrals and elliptic functions. III. Numer. Math. 13 (4), pp. 305–315.

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Notes:

Algol 60 programs for the incomplete elliptic integral of the third kind, and for a general complete elliptic integral, are included.

External Links:

ISSN 0029-599X, Document, MathReview, ZentralBlatt

Referenced by:

§19.2(iii), §19.36(ii), §19.36(ii), §19.39(ii), §19.39(iii), R. Bulirsch (1965a).

Encodings:

BibTeX

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Numerical calculation of elliptic integrals and elliptic functions. Numer. Math. 7 (1), pp. 78–90.

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Notes:

Algol 60 programs are included for real and complex elliptic integrals, and for Jacobian elliptic functions of real argument.

External Links:

ISSN 0029-599X, Document, MathReview (M. Feliciano), ZentralBlatt

Referenced by:

§19.1, §19.2(iii), §19.36(ii), §19.39(iii), §22.22(ii).

Encodings:

BibTeX

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On a generalization of Barton’s integral and related integrals of complete elliptic integrals. Math. Proc. Cambridge Philos. Soc. 101 (1), pp. 1–5.

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External Links:

ISSN 0305-0041, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§19.13(i).

Encodings:

BibTeX

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