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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
Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and q -series. …
3: 14.31 Other Applications
The conical functions P - 1 2 + i τ m ( x ) appear in boundary-value problems for the Laplace equation in toroidal coordinates14.19(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
§13.28(i) Exact Solutions of the Wave Equation
5: 12.17 Physical Applications
§12.17 Physical Applications
6: 28.32 Mathematical Applications
§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
§29.18(i) Sphero-Conal Coordinates
§29.18(ii) Ellipsoidal Coordinates
8: 31.17 Physical Applications
Then …
9: 23.21 Physical Applications
§23.21(iii) Ellipsoidal Coordinates
10: 1.5 Calculus of Two or More Variables
§1.5(ii) Coordinate Systems
Polar Coordinates
Cylindrical Coordinates
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. …