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MathGroup Archive 2007

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Re: Maclaurin series for ArcCosh[x]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73614] Re: Maclaurin series for ArcCosh[x]
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Fri, 23 Feb 2007 04:31:40 -0500 (EST)
  • References: <erjoou$p9a$1@smc.vnet.net>

Andrzej Kozlowski <akoz at mimuw.edu.pl> 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.

FWIW:
I think this does not happen because of ArcCosh in particular. For example,
Series[ArcCosh[x], {x, 1, 11}]  and  ArcCosh[x] + O[x - 1]^12  _do_ give
the same answer. I must guess the quirk you observed is due to the nature
of the series. Based on that guess, I next tried
Series[ArcCot[x], {x, 0, 11}]  and  ArcCot[x] + O[x]^12  and so immediately
found another example of that quirk.

And, Andrzej, thank you for your suggestion, in an earlier thread, about
showing that a certain hypergeometric expression is 0.

David


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