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