36 Integrals with Coalescing Saddles Properties 36.2 Catastrophes and Canonical Integrals 36.4 Bifurcation Sets

§36.3 Visualizations of Canonical Integrals

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Referenced by:: Erratum (V1.0.14) for Section 36.3
Permalink:: http://dlmf.nist.gov/36.3
See also:: Annotations for Ch.36

§36.3(i) Canonical Integrals: Modulus
§36.3(ii) Canonical Integrals: Phase

§36.3(i) Canonical Integrals: Modulus

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Keywords:: canonical integrals, visualizations of modulus
Notes:: These figures were generated by the authors.
Permalink:: http://dlmf.nist.gov/36.3.i
See also:: Annotations for §36.3 and Ch.36

See accompanying text — Figure 36.3.1: Modulus of Pearcey integral $|\Psi_{2}\left(x,y\right)|$ . Magnify 3D Help

§36.3(ii) Canonical Integrals: Phase

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Keywords:: canonical integrals, visualizations of phase
Notes:: These figures were generated by the authors.
Permalink:: http://dlmf.nist.gov/36.3.ii
See also:: Annotations for §36.3 and Ch.36

In Figure 36.3.13(a) points of confluence of phase contours are zeros of $\Psi_{2}\left(x,y\right)$ ; similarly for other contour plots in this subsection. In Figure 36.3.13(b) points of confluence of all colors are zeros of $\Psi_{2}\left(x,y\right)$ ; similarly for other density plots in this subsection.

36.2 Catastrophes and Canonical Integrals 36.4 Bifurcation Sets

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(a) $\operatorname{ph}\Psi_{3}\left(x,y,3\right)$ .	(b) $\operatorname{ph}\Psi_{3}\left(x,y,0\right)$ .

(c) $\operatorname{ph}\Psi_{3}\left(x,y,-3\right)$ .	(d) $\operatorname{ph}\Psi_{3}\left(x,y,-7.5\right)$ .


(a) Contour plot, at intervals of $\pi/4$ .	(b) Density plot.

§36.3 Visualizations of Canonical Integrals

Contents

§36.3(i) Canonical Integrals: Modulus

§36.3(ii) Canonical Integrals: Phase