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1: 36.5 Stokes Sets

§36.5 Stokes Sets

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§36.5(i) Definitions

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§36.5(ii) Cuspoids

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Elliptic Umbilic Stokes Set (Codimension three)

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§36.5(iv) Visualizations

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2: 36.3 Visualizations of Canonical Integrals

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Figure 36.3.1: Modulus of Pearcey integral $|{\mathrm{\Psi }}_2\left(x,y\right)|$.

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Figure 36.3.2: Modulus of swallowtail canonical integral function $|{\mathrm{\Psi }}_3\left(x,y,3\right)|$.

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Figure 36.3.3: Modulus of swallowtail canonical integral function $|{\mathrm{\Psi }}_3\left(x,y,0\right)|$.

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Figure 36.3.4: Modulus of swallowtail canonical integral function $|{\mathrm{\Psi }}_3\left(x,y,-3\right)|$.

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Figure 36.3.13: Phase of Pearcey integral $\mathrm{ph}{\mathrm{\Psi }}_2\left(x,y\right)$.

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3: 20 Theta Functions

Chapter 20 Theta Functions

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4: 36.4 Bifurcation Sets

§36.4 Bifurcation Sets

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Bifurcation (Catastrophe) Set for Cuspoids

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Bifurcation (Catastrophe) Set for Umbilics

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§36.4(ii) Visualizations

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5: 8 Incomplete Gamma and Related
Functions

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6: 28 Mathieu Functions and Hill’s Equation

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7: Sidebar 9.SB1: Supernumerary Rainbows

… ►Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton’s picture of light as a stream of independent corpuscles. The house in the picture is Newton’s birthplace. …

8: 8.26 Tables

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Khamis (1965) tabulates $P(a,x)$ for $a=0.05(.05)10(.1)20(.25)70$, $0.0001\le x\le 250$ to 10D.

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Abramowitz and Stegun (1964, pp. 245–248) tabulates $E_n\left(x\right)$ for $n=2,3,4,10,20$, $x=0(.01)2$ to 7D; also $(x+n){\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2,3,4,10,20$, $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

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Pagurova (1961) tabulates $E_n\left(x\right)$ for $n=0(1)20$, $x=0(.01)2(.1)10$ to 4-9S; ${\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2(1)10$, $x=10(.1)20$ to 7D; ${\mathrm{e}}^x{E}_p\left(x\right)$ for $p=0(.1)1$, $x=0.01(.01)7(.05)12(.1)20$ to 7S or 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

9: 23 Weierstrass Elliptic and Modular
Functions

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10: 36 Integrals with Coalescing Saddles

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