Re: series expansion of polys with real exponents
- To: mathgroup@smc.vnet.net
- Subject: [mg11667] Re: series expansion of polys with real exponents
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Sat, 21 Mar 1998 18:35:06 -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? D is not a good symbol to use (it denotes partial differentiation). Further to my previous posting, you can compute a series, not in positive (real) powers of x) about points other than x == 0. In fact, a plot of 2 x/(-x^0.2 - x^1.8 + 2) shows that it is singular at x == 1. Here we compute the (numerical) series about the singular point: In[1]:= Normal[2 x/(-x^0.2 - x^1.8 + 2) + O[x, 1]^4] Out[1]= 3 2 0.0284262 (x - 1) - 0.079232 (x - 1) + 0.2176 (x - 1) - 1. 0.68 - ----- x - 1 The form of the singularity is clearly shown. For x near 1, say In[2]:= % /. x -> 0.7 Out[2]= 2.58015 the approximation is quite good: In[3]:= 2 x/(-x^0.2 - x^1.8 + 2) /. x -> 0.7 Out[3]= 2.58008 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 ____________________________________________________________________