A differential-algebraic study of the intrusion of logarithms into asymptotic expansions
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Publisher SummaryThis chapter reviews a differential-algebraic study of the intrusion of logarithms into asymptotic expansions. The nonappearances of high-ranking logarithms are elementary instances of results which are obtained in the chapter., The domain of operations is a graduated logarithmic field, which, roughly speaking, is an abstract differential field having extra structure designed to provide a setting for asymptotic expansions. The rank-rise problem for asymptotic expansions is to determine, for an r-inscribed first-order differential polynomial P, how large the logarithmic rank of mn can be if mn is a term in an asymptotic expansion of a solution of P.

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