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MathGroup Archive 2007

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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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