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[1]:=
Simplify[ComplexExpand[Normal[Series[ArcSin[x], {x, 1, 4}]]], x < 1]
Out[1]=
2 3
6720 Pi + Sqrt[2 - 2 x] (14887 - 1849 x + 477 x - 75 x )
---------------------------------------------------------
13440
or if you prefer:
In[2]:=
Expand[%]
Out[2]=
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[53]:= Series[ArcSin[x],{x,1,4}]
>
> I 3/2 3 I 5/2
> - (-1 + x) --- (-1 + x)
> Pi 6 80
> Out[53]= -- - I Sqrt[2] Sqrt[-1 + x] + ------------- - --------------- +
> 2 Sqrt[2] Sqrt[2]
>
> 5 I 7/2
> --- (-1 + x)
> 448 9/2
>> --------------- + O[-1 + x]
> Sqrt[2]
>
> 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
>
>
>