Series Expansion Inconsistency
- To: mathgroup at yoda.physics.unc.edu
- Subject: Series Expansion Inconsistency
- From: Cetin Cetinkaya <cetin at acm0.me.uiuc.edu>
- Date: Mon, 19 Apr 1993 20:19:27 -0500
Hello;
While I am trying to do some perturbation analysis, I run into a peculiar
behaviour. My function k looks like
In[31]:= k
0. Second 1928.568 KByte
3 - n 3 - n
(c1 eps) - (c20 + c21 eps)
Out[31]= -------------------------------------------------------------
2 - n 2 - n
c1 eps (c20 + c21 eps) ((c1 eps) - (c20 + c21 eps) )
For n=19, I expand the function k with respect to eps up to eps^2 and
collect the coefficients of eps:
In[32]:= Collect[Simplify[Normal[Series[k/.n->19,{eps,0,2}]]] ,eps]
3.15 Second 1929.216 KByte
1
Out[32]= ---
c20
This simply means that the expansion does not have eps or eps^2 orders
terms. However, When I tried the following to see how the eps^3 order
term looks like, I have got this:
In[33]:= Collect[Simplify[Normal[Series[k/.n->19,{eps,0,3}]]] ,eps]
3.81667 Second 1930.156 KByte
2 2 3 3
1 c21 eps c21 eps c21 eps
Out[33]= --- - ------- + --------- - ---------
c20 2 3 4
c20 c20 c20
To my suprise, this expression has order eps and eps^2 terms. Could any
one explain what is going on?
The Mathematica verson I am running is 2.1.
Cetin