Re: series expansion of polys with real exponents
- To: mathgroup@smc.vnet.net
- Subject: [mg11665] Re: series expansion of polys with real exponents
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Sat, 21 Mar 1998 18:35:04 -0500
- Organization: University of Western Australia
- References: <6esp6s$699@smc.vnet.net>
Hafeez Abdulrauf wrote: > I would like to find the series expansion of an expression like > > 2 D / (2 -D^0.2 -D^1.8) > > in positive (real) powers of D. As the expression has real exponents on > D, it's not really a polynomial and none of the polynomial functions > work here. Is there any way to work it out? No (ordinary) series expansion exists. However, for this particular example, if your exponents 0.2 and 1.8 were "exact" then you could proceed as follows: In[1]:= 2 x/(2 - x^(1/5) - x^(9/5) + O[x]^4//Normal Out[1]= 19/5 18/5 17/5 16/5 3 1537 x 1281 x 1025 x 769 x 513 x ---------- + ---------- + ---------- + --------- + ------ + 16384 8192 4096 2048 1024 14/5 13/5 12/5 11/5 2 9/5 8/5 257 x x x x x x x --------- + ----- + ----- + ----- + -- + ---- + ---- + 512 256 128 64 32 16 8 7/5 6/5 x x ---- + ---- + x 4 2 This approximation is slowly-convergent In[2]:= % /. x -> 0.1 Out[2]= 0.146879 which should be compared with In[3]:= 2 x/(-x^1.8 - x^0.2 + 2) /. x -> 0.1 Out[3]= 0.147798 Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul@physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________