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1: 19.32 Conformal Map onto a Rectangle

… ►then $z(p)$ is a Schwartz–Christoffel mapping of the open upper-half $p$-plane onto the interior of the rectangle in the $z$-plane with vertices …

2: 30.14 Wave Equation in Oblate Spheroidal Coordinates

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§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids

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3: 14.28 Sums

… ►where ${ℰ}_1$ and ${ℰ}_2$ are ellipses with foci at $\pm 1$, ${ℰ}_2$ being properly interior to ${ℰ}_1$. …

4: 30.13 Wave Equation in Prolate Spheroidal Coordinates

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§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids

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5: 23.20 Mathematical Applications

… ►The interior of $R$ is mapped one-to-one onto the lower half-plane. … ►The interior of the rectangle with vertices $0$, ${\omega }_1$, $2{\omega }_3$, $2{\omega }_3-{\omega }_1$ is mapped two-to-one onto the lower half-plane. The interior of the rectangle with vertices $0$, ${\omega }_1$, $\frac{1}{2}{\omega }_1+{\omega }_3$, $\frac{1}{2}{\omega }_1-{\omega }_3$ is mapped one-to-one onto the lower half-plane with a cut from $e_3$ to $\mathrm{\wp }\left(\frac{1}{2}{\omega }_1+{\omega }_3\right)(=\mathrm{\wp }\left(\frac{1}{2}{\omega }_1-{\omega }_3\right))$. …

6: 2.4 Contour Integrals

… ►We assume that in any closed sector with vertex $t=0$ and properly interior to , the expansion (2.3.7) holds as $t\to 0$, and $q(t)=O\left({\mathrm{e}}^{\sigma |t|}\right)$ as $t\to \mathrm{\infty }$, where $\sigma$ is a constant. Then (2.4.1) is valid in any closed sector with vertex $z=0$ and properly interior to . … ►Now suppose that in (2.4.10) the minimum of $\mathrm{\Re }\left(zp(t)\right)$ on $𝒫$ occurs at an interior point $t_0$. … ►In the commonest case the interior minimum $t_0$ of $\mathrm{\Re }\left(zp(t)\right)$ is a simple zero of $p^{\prime }(t)$. …

7: 1.9 Calculus of a Complex Variable

… ►Points of a region that are not boundary points are called interior points. … ►

Jordan Curve Theorem

… ►One of these domains is bounded and is called the interior domain of $C$; the other is unbounded and is called the exterior domain of $C$. …

8: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, $F_{\mathrm{\ell }}(\eta ,\rho )$ and $G_{\mathrm{\ell }}(\eta ,\rho )$, or $f(ϵ,\mathrm{\ell };r)$ and $h(ϵ,\mathrm{\ell };r)$, to determine the scattering $S$-matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951). …

9: 3.4 Differentiation

… ►where $C$ is a simple closed contour described in the positive rotational sense such that $C$ and its interior lie in the domain of analyticity of $f$, and $x_0$ is interior to $C$. …

10: Bibliography

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High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder. J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.

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§36.14(ii).

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