Talk:Asymptotic expansion

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For an asymptotic scale, I also know the definition of an (arbitrary) family of functions S={f_{m} such that}

_{Then this induces an evident ordering on the set of indices, and asymptotic expansions are defined in the same way, as finite sums on m≥ m' , such that the difference is negligible w.r.t. all m<m' .}

_{Without being too general, we should allow at least for negative indices, e.g. for Laurent series, but maybe there is really a need for an indexing set other than N, in order to be able to develop on the scale x^a(log x)^b. for example. — MFH: Talk 14:00, 24 May 2005 (UTC)}

_{Yes. There is quite a big subject - orders of infinity. Charles Matthews 11:38, 25 May 2005 (UTC)}

_{[edit] the definition}

_{I think that}

_{is unnecessarily limiting. I think this is enough:}

_{If you agree, pls change it. --Zero 14:58, 22 August 2005 (UTC)}

_{[edit] differentiation and integration}

_{My question is if we have}

_{f(x)˜g(x) then is correct that:}

_{f'(x)˜g'(x) or}

_{In several books i have read that this is true, however i'm not completely sure though. —The preceding unsigned comment was added by 85.85.100.144 (talk) 09:52, 11 January 2007 (UTC).}

_{The first one is certainly not true: imagine that 'g' is the same as 'f' except that it has very fine wriggles that get smaller quickly but not flatter. The second one might be true most of the time, perhaps with some sanity conditions required. --Zero^talk 12:09, 11 January 2007 (UTC)}

_{[edit] another example}

_{Stirling's approximation is another important example - should it be added to the main page? Lavaka 00:23, 15 February 2007 (UTC)}