Re: Need help to a beginner.
- To: mathgroup at smc.vnet.net
- Subject: [mg9657] Re: Need help to a beginner.
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 21 Nov 1997 01:30:56 -0500
- Organization: University of Western Australia
- Sender: owner-wri-mathgroup at wolfram.com
Shinichiro Kondo wrote: > First of all, let me explain my problem. It is known, if you expand > 1/Sqrt[1-x], provided that x^2<<1, you have > 1+(1/2)*x+(3/*)*x^2+(5/16)*x^3+.... Now, let's have a similar > expression to this: 1/Sqrt[(a-x)^2+y^2+z^2]. > Suppose x, y and z are cartesian coordinates, and r^2=x^2+y^2+z^2. And a > is some positive constant, and it satisfies a>>r. So factoring the > denominator by a^2 and kicking it out of the Sqrt as a, I can continue > this algebra by my hand, and I should end up with: > (1/a)*(1+x/a-r^2/(2*a^2)+(3*x^2)/(2*a^2)+....) in which I only keep up > to the 2nd order of r/a (and x/a). > > I would like to be able to do this by Mathematica. That is, given this > sort of a reciprocal of a Sqrt of quadratic expression with x, y and z, > I'd like it to expand "approximately" so that a resultant expression > only contain the terms up to a specified order of r/a (thus, x/a, y/a, > and z/a). How can I do this? This kind of expansion goes on forever, > but I don't need many higher order terms. How can I specify the maximum > order that I want to have? Look up Series in Mathematica. Here is one way to do what you want: In[1]:= Simplify[1/Sqrt[(a - x)^2 + y^2 + z^2] + O[a, Infinity]^5 /. y^2 -> r^2 - x^2 - z^2] Out[1]= 2 2 2 3 -r 3 x -3 r x 5 x --- + ---- ------- + ---- 1 x 2 2 2 2 1 5 - + -- + ---------- + -------------- + O[-] a 2 3 4 a a a a 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 at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________