RE: Need help to a beginner.
- To: mathgroup at smc.vnet.net
- Subject: [mg9668] RE: [mg9642] Need help to a beginner.
- From: jmthomas <jmthomas at cybercable.tm.fr>
- Date: Fri, 21 Nov 1997 01:31:06 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Try this:
args=Expand[(a-x)^2+y^2+z^2]/.x^2+y^2+z^2->r f=1/Sqrt[args]
Series[f,{x,0,3},{r,0,3}]
If you want to get a polynomial expression, use Normal. Hope this helps.
----------------------------------------------- Jean-Marie THOMAS
Conseil et Audit en Ingenierie de Calcul jmthomas at cybercable.tm.fr
+33 (0)3 88 32 93 64
www.cybercable.tm.fr/~jmthomas
=======================
-----Original Message-----
From: Shinichiro Kondo [SMTP:shink at iastate.edu] To:
mathgroup at smc.vnet.net
Sent: Tuesday, November 18, 1997 1:50 AM To: mathgroup at smc.vnet.net
Subject: [mg9642] Need help to a beginner.
Hi, all. I am quite new to Mathematica, and am using the older version,
v. 2.2. I hope someone will help me. My problem is nothing to do with
homework of a math class, or any sort. I am a physics graduate student,
and for my research project am trying to have an algebraic expression
of potential energy of certain ionic crystalline lattice. The
electrostatic (i.e. Coulomb) energy has the expression of 1/r, where r
is the distance between two charges. I am still far from getting the
answer I want because of this problem I am facing in the very first
stage where I am supposed to be used to Mathematica.
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?
I will greatly appreciate someone's help to this problem. Meanwhile, I
am trying to find a solution in the manual by myself. If you don't
mind, please send your solution to my email address: shink at iastate.edu
Thank you for your attention.