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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       
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http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________



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