Re: Bug in interpretation of mma Series[] command?

*To*: mathgroup at smc.vnet.net*Subject*: [mg2299] Re: Bug in interpretation of mma Series[] command?*From*: Paul Abbott <paul at earwax.pd.uwa.edu.au>*Date*: Mon, 23 Oct 1995 12:42:06 -0400*Organization*: Dept of Physics, University of WA

siegman at ee.stanford.edu (A. E. Siegman) wrote: >Does the following make sense to anyone? > > In[6]:= > f[y] = Exp[-a y^2] * Series[1/(1 + y^2), {y,0,5}] > > Out[6]= > 2 > 2 a 4 6 > 1 + (-1 - a) y + (1 + a + --) y + O[y] > 2 > >This strikes me as a really counter-intuitive, perverse, >guaranteed-to-cause-trouble "gotcha". Totally disagree! The fact that the presence of an O[y] term AUTOMATICALLY coerces the result into a series is a beautiful and useful syntax. For example, see what happens when you enter f[x] + O[x]^5 >... but the first case should surely >either generate an error msg, or not be interpreted at >all. Why? >There's no way any sensible interpretation of >the input command (by normal users, that is) should lead >to series expansion of the Exp[] function also. Yes there is -- whenever you have performed a Series expansion the result is a special (SeriesData) object. Any further manipulutations of this object (including muliplying by an arbitrary function) works as expected. E.g., f[x]+O[x]^3 1/% I take advantage of this syntax all the time. Cheers, Paul