Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2000
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
> 
> 
> 



  • Prev by Date: Re: Distance between permutations
  • Next by Date: Re: Flat, OneIdentity attributes
  • Previous by thread: Re: Series expansion of ArcSin around 1
  • Next by thread: Re: Series expansion of ArcSin around 1