       Re: Series expansion of ArcSin around 1

• To: mathgroup at smc.vnet.net
• Subject: [mg21623] Re: [mg21598] Series expansion of ArcSin around 1
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Tue, 18 Jan 2000 02:35:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Is the following satisfactory?

In:=
Simplify[ComplexExpand[Normal[Series[ArcSin[x], {x, 1, 4}]]], x < 1]

Out=
2       3
6720 Pi + Sqrt[2 - 2 x] (14887 - 1849 x + 477 x  - 75 x )
---------------------------------------------------------
13440

or if you prefer:

In:=
Expand[%]

Out=
Pi   14887 Sqrt[2 - 2 x]   1849 Sqrt[2 - 2 x] x
-- + ------------------- - -------------------- +
2           13440                 13440

2
159 Sqrt[2 - 2 x] x     5                 3
-------------------- - --- Sqrt[2 - 2 x] x
4480           896

> From: Jacek Pliszka <pliszka at fuw.edu.pl>
To: mathgroup at smc.vnet.net
> Date: Sun, 16 Jan 2000 22:43:46 -0500 (EST)
> To: mathgroup at smc.vnet.net
> Subject: [mg21623] [mg21598] Series expansion of ArcSin around 1
>
> 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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