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1: 16.8 Differential Equations

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§16.8(iii) Confluence of Singularities

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2: 31.12 Confluent Forms of Heun’s Equation

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3: 35.8 Generalized Hypergeometric Functions of Matrix Argument

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Confluence

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4: 36.3 Visualizations of Canonical Integrals

… ►In Figure 36.3.13(a) points of confluence of phase contours are zeros of ${\mathrm{\Psi }}_2\left(x,y\right)$; similarly for other contour plots in this subsection. In Figure 36.3.13(b) points of confluence of all colors are zeros of ${\mathrm{\Psi }}_2\left(x,y\right)$; similarly for other density plots in this subsection. …

5: 2.4 Contour Integrals

… ►The function $f(\alpha ,w)$ is analytic at $w=w_1(\alpha )$ and $w=w_2(\alpha )$ when $\alpha \ne \widehat{\alpha }$, and at the confluence of these points when $\alpha =\widehat{\alpha }$. …

6: 3.3 Interpolation

… ►Another advantage is its robustness with respect to confluence of the set of points $z_0,z_1,\mathrm{\dots },z_n$. …