Analytic
Usage Message: Analytic is an option for Limit and Series. With Analytic -> True, unrecognized functions are treated
as analytic, and processed using Taylor series expansions; with Analytic -> False, Taylor series are not used unless the function is recognized as analytic.
Attributes[Analytic] = {Protected} Related Symbols: Limit
, Series
Notes: Analytic is an option in Limit and Series which indicates whether or not derivatives should be used to compute the coefficients in series expansions of unknown functions. With Analytic -> False derivatives are not used, and the limit or series calculation will normally fail. With Analytic -> True, the calculation will proceed using derivatives of the unknown function.
In[1]:= Limit[(f[x + a] - f[a])/x, x -> 0, Analytic -> False]
-f[a] + f[a + x]
Out[1]= Limit[----------------, x -> 0, Analytic -> False]
x
In[2]:= Limit[(f[x + a] - f[a])/x, x -> 0, Analytic -> True]
Out[2]= f'[a]
The Analytic option has not been fully implemented for Series, and although it changes the order in which certain internal calculations are done, it normally has no effect on results. Analytic -> False prevents the Series from using derivatives to compute series expansions for unknown functions, but it does not prevent up-code or up-values for SeriesData from using derivatives, since since much of the computation of series is based on up-code and up-values for SeriesData, derivatives will be used to compute the result regardless of the value of the Analytic option.
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