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