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Re: Series expansion of ArcSin around 1
*To*: mathgroup at smc.vnet.net
*Subject*: [mg21638] Re: [mg21598] Series expansion of ArcSin around 1
*From*: "Mark Harder" <harderm at ucs.orst.edu>
*Date*: Tue, 18 Jan 2000 02:35:22 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Jacek,
I don't know how to get Mathematica to modify its expansion for the
restricted case x=real; but if you need to compute with Series, you can
convert to Normal form and replace x with values, or you can extract the
real part of the normal form and then replace. i.e.:
In[30]:=ts=Simplify[Series[ArcSin[x],{x,1,4}] ];
Normal[ts]/.x->.99
Re[%]
Out[31]=1.71233580011662844` +0.` I
Out[32]=1.71233580011662844`
or
In[33]:=Re[Normal[ts]];
%/.x->.99
Out[34]=1.71233580011662844`
-mark
-----Original Message-----
From: Jacek Pliszka <pliszka at fuw.edu.pl>
To: mathgroup at smc.vnet.net
Subject: [mg21638] [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
>
>
>
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