Summary
It is shown that for azimuthal wave numbers and period 0.5 (s+1) days, Hough's functions for tidal oscillations are the same as the associated Legendre polynomialsP ss+1 and Hough's functions are shown to form a complete set of orthogonal functions. The implication of this on the vertical variation of tides is discussed.
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Giwa, F.B.A. The ‘missing’ member of Hough's functions in diurnal tides. PAGEOPH 112, 519–522 (1974). https://doi.org/10.1007/BF00877288
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DOI: https://doi.org/10.1007/BF00877288