Inverse Prolate Spheroidal Coordinates

A system of coordinates obtained by inversion of the prolate spheroids and two-sheeted hyperboloids in prolate spheroidal coordinates. The inverse prolate spheroidal coordinates are given by the transformation equations

			(1)
			(2)
			(3)

with , , and . Surfaces of constant are given by the cyclides of rotation

(4)

surfaces of constant by the cyclides of rotation

(5)

and surfaces of constant by the half-planes

(6)

The metric coefficients are given by

			(7)
			(8)
			(9)

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