Re: Maclaurin series for ArcCosh[x] (update!)

*To*: mathgroup at smc.vnet.net*Subject*: [mg73642] Re: Maclaurin series for ArcCosh[x] (update!)*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 23 Feb 2007 04:46:49 -0500 (EST)*References*: <erjoou$p9a$1@smc.vnet.net>

Hi again. Note the following Series[ArcCosh[x], {x, 0, 11}, Assumptions -> x =E2=88=88 Reals] SeriesData[x, 0, {(I/2)*Pi, -I, 0, -I/6, 0, (-3*I)/40, 0, (-5*I)/112, 0, (-35*I)/1152, 0, (-63*I)/2816}, 0, 12, 1] ArcCosh[x] + O[x]^12 ArcCosh[x] + SeriesData[x, 0, {}, 12, 12, 1] But applying first the TrigToExp function we get TrigToExp[ArcCosh[x]] + O[x]^12 SeriesData[x, 0, {(I/2)*Pi, -I, 0, -I/6, 0, (-3*I)/40, 0, (-5*I)/112, 0, (-35*I)/1152, 0, (-63*I)/2816}, 0, 12, 1] Regards Dimitris =CE=9F/=CE=97 Andrzej Kozlowski =CE=AD=CE=B3=CF=81=CE=B1=CF=88=CE=B5: > Try: > > Series[ArcCosh[x], {x, 0, 11}] > > and now try > > ArcCosh[x] + O[x]^12 > > At least with my version of Mathematica: > > $Version > 5.2 for Mac OS X (February 24, 2006) > > > I do not get the same answer (in fact in the latter case the input is > returned unevaluated). With ArcSinh and any other function that I > have tried in place of ArcCosh the outputs are always the same. > > Andrzej Kozlowski