       Series expansion of ArcSin around 1

• To: mathgroup at smc.vnet.net
• Subject: [mg21598] Series expansion of ArcSin around 1
• From: Jacek Pliszka <pliszka at fuw.edu.pl>
• Date: Sun, 16 Jan 2000 22:43:46 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi!

I have the following problem. My x is close to 1 but sligthly
smaller. I want to expand ArcSin[x] around 1 but this is what I get:

In:= Series[ArcSin[x],{x,1,4}]

I         3/2   3 I         5/2
- (-1 + x)      --- (-1 + x)
Pi                            6               80
Out= -- - I Sqrt Sqrt[-1 + x] + ------------- - --------------- +
2                                Sqrt          Sqrt

5 I         7/2
--- (-1 + x)
448                        9/2
>    --------------- + O[-1 + x]
Sqrt

How to tell Mathematica that my x is real and smaller than 1
so it will not return all this complex numbers?

Thanks for any help,

Jacek

```

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