Re: Series expansion of ArcSin around 1

• To: mathgroup at smc.vnet.net
• Subject: [mg21636] Re: Series expansion of ArcSin around 1
• From: John Doty <jpd at w-d.org>
• Date: Tue, 18 Jan 2000 02:35:20 -0500 (EST)
• References: <85u3a4\$d5d@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jacek Pliszka wrote:

> In[53]:= Series[ArcSin[x],{x,1,4}]
> ...
> How to tell Mathematica that my x is real and smaller than 1
> so it will not return all this complex numbers?

Your problem is that Series uses (x-1) as the base. It's negative in
your range, and since the series involves noninteger powers of the base
you wind up with complex expressions representing real numbers. You can
coax Series into using (1-x) as the base by a change of variable:

Series[ArcSin[-y],{y,-1,4}]/.y->-x

--
John Doty		"You can't confuse me, that's my job."
Home: jpd at w-d.org
Work: jpd at space.mit.edu

```

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