       Re: Maclaurin series for ArcCosh[x] (update!)

• To: mathgroup at smc.vnet.net
• Subject: [mg73642] Re: Maclaurin series for ArcCosh[x] (update!)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Fri, 23 Feb 2007 04:46:49 -0500 (EST)
• References: <erjoou\$p9a\$1@smc.vnet.net>

Hi again.

Note the following

Series[ArcCosh[x], {x, 0, 11}, Assumptions -> x =E2=88=88 Reals]
SeriesData[x, 0, {(I/2)*Pi, -I, 0, -I/6, 0, (-3*I)/40, 0, (-5*I)/112,
0, (-35*I)/1152, 0, (-63*I)/2816}, 0, 12, 1]

ArcCosh[x] + O[x]^12
ArcCosh[x] + SeriesData[x, 0, {}, 12, 12, 1]

But applying first the TrigToExp function we get

TrigToExp[ArcCosh[x]] + O[x]^12
SeriesData[x, 0, {(I/2)*Pi, -I, 0, -I/6, 0, (-3*I)/40, 0, (-5*I)/112,
0, (-35*I)/1152, 0, (-63*I)/2816}, 0, 12, 1]

Regards
Dimitris

> 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.
>
> Andrzej Kozlowski

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