Re: Pb Limit ArcTan to : - Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg34645] Re: [mg34624] Pb Limit ArcTan to : - Infinity
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Fri, 31 May 2002 04:26:20 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
i think the answer is that Series does not expand around -Infinity, only
about Infinity. Presumably this is because the expansions are meant to
be interpreted as given in the complex plane. You can check that using
-Infinity and Infinity gives the same series (at least in all the cases
I have checked). However, you can always use:
In[16]:=
Normal[Series [ ArcTan [ -x ] , { x , Infinity , 2 }]]
Out[16]=
Pi 1
-(--) + -
2 x
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Thursday, May 30, 2002, at 03:55 PM, Didier Losfeld wrote:
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> Bonjour ,
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> I do not understand answers of Mathematica :
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> question 1 : Series [ ArcTan [ x ] , { x , - Infinity , 2 } ]
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> answer : Pi / 2 - 1 / x + O ( 1 / x ) ^ 3
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> question 2 : Limit [ ArcTan [ x ] , x -> - Infinity ]
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> answer : - Pi / 2
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> The first answer is False , the second answer is correct.
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> Many thanks in advance.
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> Didier Losfeld Professor of mathematics ( France )
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