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MathGroup Archive 1998

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Re: Pulling out certain order terms from a polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg12967] Re: Pulling out certain order terms from a polynomial
  • From: Daniel Lichtblau <danl>
  • Date: Sun, 28 Jun 1998 02:51:55 -0400
  • Organization: Wolfram Research, Inc.
  • References: <6mqa3p$2qo@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Might try to build the series in each variable separately. For the
second variable, build sub-series in each term in the series in the
first variable, only taking as many terms as appropriate.

In[8]:= s1 = Series[Exp[u+Sin[v]], {u,0,8}]
                               Sin[v]  2    Sin[v]  3    Sin[v]  4
         Sin[v]    Sin[v]     E       u    E       u    E       u
Out[8]= E       + E       u + ---------- + ---------- + ---------- +
                                  2            6            24
      Sin[v]  5    Sin[v]  6    Sin[v]  7    Sin[v]  8
     E       u    E       u    E       u    E       u        9
>    ---------- + ---------- + ---------- + ---------- + O[u]
        120          720          5040        40320

In[9]:= s1[[3]] = MapIndexed[Series[#1,{v,0,First[8-#2+1]}]&, s1[[3]]];

In[10]:= s1
                  2    4    5    6     7       8
                 v    v    v    v     v    31 v        9
Out[10]= 1 + v + -- - -- - -- - --- + -- + ----- + O[v]  +
                 2    8    15   240   90   5760
               2    4    5    6     7
              v    v    v    v     v        8
>    (1 + v + -- - -- - -- - --- + -- + O[v] ) u +
              2    8    15   240   90
               2    4    5    6
      1   v   v    v    v    v         7   2
>    (- + - + -- - -- - -- - --- + O[v] ) u  +
      2   2   4    16   30   480
               2    4    5                           2    4
      1   v   v    v    v        6   3    1    v    v    v         5   4
>    (- + - + -- - -- - -- + O[v] ) u  + (-- + -- + -- - --- + O[v] ) u  +
      6   6   12   48   90                24   24   48   192
                   2                               2
       1     v    v         4   5     1     v     v         3   6
>    (--- + --- + --- + O[v] ) u  + (--- + --- + ---- + O[v] ) u  +
      120   120   240                720   720   1440
       1      v         2   7      1            8       9
>    (---- + ---- + O[v] ) u  + (----- + O[v]) u  + O[u]
      5040   5040                40320


If you do not require a SeriesData result, there are other ways to
approach this that begin by using Normal to get a polynomial.
                                                                        


Daniel Lichtblau
Wolfram Research


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