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1: 29.18 Mathematical Applications
§29.18(i) Sphero-Conal Coordinates
when transformed to sphero-conal coordinates r , β , γ : …
29.18.4 u ( r , β , γ ) = u 1 ( r ) u 2 ( β ) u 3 ( γ ) ,
29.18.5 d d r ( r 2 d u 1 d r ) + ( ω 2 r 2 - ν ( ν + 1 ) ) u 1 = 0 ,
29.18.6 d 2 u 2 d β 2 + ( h - ν ( ν + 1 ) k 2 sn 2 ( β , k ) ) u 2 = 0 ,