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1: 28.27 Addition Theorems

… ►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …

2: Howard S. Cohl

… ►His research interests include fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre and Jacobi functions, generalized and basic hypergeometric functions, eigenfunction expansions in separable coordinate systems, generating functions, $q$-series, and orthogonal polynomials in the Askey and $q$-Askey schemes. …

3: 14.31 Other Applications

… ►The conical functions ${𝖯}_{-\frac{1}{2}+\mathrm{i}\tau }^m\left(x\right)$ appear in boundary-value problems for the Laplace equation in toroidal coordinates (§14.19(i)) for regions bounded by cones, by two intersecting spheres, or by one or two confocal hyperboloids of revolution (Kölbig (1981)). …

4: 13.28 Physical Applications

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§13.28(i) Exact Solutions of the Wave Equation

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5: 12.17 Physical Applications

§12.17 Physical Applications

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6: 28.32 Mathematical Applications

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§28.32(i) Elliptical Coordinates and an Integral Relationship

… ►Kernels $K$ can be found, for example, by separating solutions of the wave equation in other systems of orthogonal coordinates. … ►

§28.32(ii) Paraboloidal Coordinates

►The general paraboloidal coordinate system is linked with Cartesian coordinates via …

7: 29.18 Mathematical Applications

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§29.18(i) Sphero-Conal Coordinates

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§29.18(ii) Ellipsoidal Coordinates

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8: 31.17 Physical Applications

… ►Then …

9: 23.21 Physical Applications

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§23.21(iii) Ellipsoidal Coordinates

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10: 1.5 Calculus of Two or More Variables

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§1.5(ii) Coordinate Systems

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Polar Coordinates

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Cylindrical Coordinates

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Spherical Coordinates

… ►For applications and other coordinate systems see §§12.17, 14.19(i), 14.30(iv), 28.32, 29.18, 30.13, 30.14. …