Pearcey%20integral

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1: 36.5 Stokes Sets

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§36.5(ii) Cuspoids

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36.5.7 $$X=\frac{9}{20}+20u^4-\frac{Y^2}{20u^2}+6u^2\mathrm{sign}\left(z\right),$$

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Symbols:

$\mathrm{sign}x$: sign of, $z$: real parameter, $X$: scaled coordinate and $Y$: scaled coordinate

Permalink:

http://dlmf.nist.gov/36.5.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §36.5(ii), §36.5(ii), §36.5 and Ch.36

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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. …

2: 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:

BibTeX

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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.

Encodings:

BibTeX

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A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey’s integral and its derivatives. J. Phys. A 15 (4), pp. 1179–1190.

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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§36.15(iii), §36.8.

Encodings:

BibTeX

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Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey’s integral and its derivatives. Chem. Phys. Lett. 81 (2), pp. 306–310.

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External Links:

ISSN 0009-2614, Document, MathReview (J. S. Joel)

Referenced by:

§36.14(iii).

Encodings:

BibTeX

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3: Bibliography P

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The asymptotic behaviour of Pearcey’s integral for complex variables. Proc. Roy. Soc. London Ser. A 432 (1886), pp. 391–426.

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External Links:

ISSN 0962-8444, Document, Link, MathReview (J. S. Joel), ZentralBlatt

Referenced by:

§36.12(i).

Encodings:

BibTeX

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The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic. Philos. Mag. (7) 37, pp. 311–317.

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External Links:

MathReview (C. J. Bouwkamp)

Referenced by:

§36.2(ii).

Encodings:

BibTeX

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Numerical calculation of the generalized Fermi-Dirac integrals. Comput. Phys. Comm. 55 (2), pp. 127–136.

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External Links:

Document

Referenced by:

§25.18(i).

Encodings:

BibTeX

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

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Elliptic integrals. Computers in Physics 4 (1), pp. 92–96.

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Referenced by:

2nd item.

Encodings:

BibTeX

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4: 36.2 Catastrophes and Canonical Integrals

§36.2 Catastrophes and Canonical Integrals

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Canonical Integrals

… ► ${\mathrm{\Psi }}_2$ is the Pearcey integral (Pearcey (1946)): … … ►

§36.2(iii) Symmetries

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5: Bibliography K

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On the zeroes of the Pearcey integral. J. Comput. Appl. Math. 107 (1), pp. 31–52.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§36.7(ii), §36.7(ii).

Encodings:

BibTeX

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

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The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.

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External Links:

ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§18.26(v), §18.26(v).

Encodings:

BibTeX

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