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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