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 > > >