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RE : Bug in O[x]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg48264] RE : [mg48233] Bug in O[x]
*From*: "Florian Jaccard" <florian.jaccard at eiaj.ch>
*Date*: Thu, 20 May 2004 04:03:39 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Hello Boris,
No, everything is alright !
You have to consider O[x] as somethig of the form a*x , O[x]^2 as something
of the form a*x^n , etc.
Rule : O[x]+O[x^2]=O[x] etc.
(1+O[x])^2=1+2*O[x]+O[x]^2=1+2*O[x]=1+O[x]
(1/x+O[x])^2=1/x^2+2*1/x*O[x]+O[x]^2=1/x^2+2*1/x*O[x]=x^(-2)+O[x]^0
(because 1/x * O[x] is something behaving like a constant...)
(1+O[x])^3=1+3*O[x]+3*O[x]^2+O[x]^3=1+O[x]
Nothing is wrong... you just d'd'nt understand the meaning of O[x]...
O[x]^n represents a term of order x^n. O[x]^n is generated to represent \
omitted higher-order terms in power series.
Regards
F.Jaccard
-----Message d'origine-----
De : Boris_Hollas [mailto:No.hollas at informatik.uni-ulm.de.Spam]
Envoyé : mercredi, 19. mai 2004 08:42
À : mathgroup at smc.vnet.net
Objet : [mg48233] Bug in O[x]
Have a look at this:
Mathematica 5.0 for Linux
Copyright 1988-2003 Wolfram Research, Inc.
-- Motif graphics initialized --
In[1]:= (1+O[x])^2
Out[1]= 1 + O[x]
In[2]:= (1/x+O[x])^2
-2 0
Out[2]= x + O[x]
In[3]:= (1+O[x])^3
Out[3]= 1 + O[x]
Obviously something is wrong with the O function in Mathematica 5.
Boris Hollas
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