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All statements involving O, o, and asymptotic expansions are based on the definitions in Erdélyi (1956)(4).
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Ogilvie, T.F. Nonlinear high-froude-number free-surface problems. J Eng Math 1, 215–235 (1967). https://doi.org/10.1007/BF01540946
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DOI: https://doi.org/10.1007/BF01540946