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

```

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