Abstract
A procedure has been devised to construct a solution of the Clairaut equation in the form of an asymptotic expansion in terms of descending powers of\(\lambda = j + \tfrac{1}{2}\), wherej denotes the order of spherical-harmonic distortion. It has been shown that asj and, therefore λ increases, the foregoing series approaches asymptotically a solution of our equation. The procedure is similar to the WKB-method of theoretical physics.
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Kopal, Z., Lanzano, P. Asymptotic solutions for the Clairaut equation in the theory of rotating fluid masses. Astrophys Space Sci 23, 425–429 (1973). https://doi.org/10.1007/BF00645169
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DOI: https://doi.org/10.1007/BF00645169