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