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paraboloidal coordinates

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1: 13.28 Physical Applications
§13.28(i) Exact Solutions of the Wave Equation
The reduced wave equation 2 w = k 2 w in paraboloidal coordinates, x = 2 ξ η cos ϕ , y = 2 ξ η sin ϕ , z = ξ - η , can be solved via separation of variables w = f 1 ( ξ ) f 2 ( η ) e i p ϕ , where …
2: 28.32 Mathematical Applications
§28.32(ii) Paraboloidal Coordinates
The general paraboloidal coordinate system is linked with Cartesian coordinates via …
3: 12.17 Physical Applications
In a similar manner coordinates of the paraboloid of revolution transform the Helmholtz equation into equations related to the differential equations considered in this chapter. … …