Re: Maclaurin series for ArcCosh[x]
- To: mathgroup at smc.vnet.net
- Subject: [mg73601] Re: Maclaurin series for ArcCosh[x]
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 23 Feb 2007 04:24:37 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <erjoou$p9a$1@smc.vnet.net>
Andrzej Kozlowski wrote: > 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. Hi Andrzej, Same behavior on my system. In[1]:= $Version Out[1]= 5.2 for Microsoft Windows (June 20, 2005) In[2]:= Series[ArcCosh[x], {x, 0, 11}] Out[2]= Floor[Arg[x]/(2 Pi)] (-1) SeriesData[Global`x, 0, I -I -3 I -5 I -35 I {- Pi, -I, 0, --, 0, ----, 0, ----, 0, -----, 0, 2 6 40 112 1152 -63 I -----}, 0, 12, 1] 2816 In[3]:= ArcCosh[x] + O[x]^12 Out[3]= ArcCosh[x] + SeriesData[Global`x, 0, {}, 12, 12, 1] In[4]:= Series[ArcSinh[x], {x, 0, 11}] Out[4]= SeriesData[Global`x, 0, 1 3 5 35 {1, 0, -(-), 0, --, 0, -(---), 0, ----, 0, 6 40 112 1152 63 -(----)}, 1, 12, 1] 2816 In[5]:= ArcSinh[x] + O[x]^12 Out[5]= SeriesData[Global`x, 0, 1 3 5 35 {1, 0, -(-), 0, --, 0, -(---), 0, ----, 0, 6 40 112 1152 63 -(----)}, 1, 12, 1] 2816 Regards, Jean-Marc