A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis which is relabeled the z-axis. The third set of coordinates consists of planes passing through this axis. x | = | a cosh ξ cos η cos ϕ y | = | a cosh ξ cos η sin ϕ z | = | a sinh ξ sin η, where ξ element [0, ∞), η element [-π/2, π/2], and ϕ element [0, 2π). Arfken uses (u, v, φ) instead of (ξ, η, ϕ).
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