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Algebraic substitution 
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#1
May1307, 07:33 AM

Mentor
P: 8,309

1. The problem statement, all variables and given/known data
I have this function [tex]F(r)=\frac{(rr_+)(rr_)}{r^2}[/tex] and I want to make the subsitution [itex]r=r_+(1+\rho^2)[/itex]. 2. Relevant equations None. 3. The attempt at a solution So, I sub in, to obtain [tex]F=\frac{[r_+(1+\rho^2)r_][r_+(1+\rho^2)r_]}{r_+^2(1+\rho^2)^2}=\frac{\rho^2[r_+(1+\rho^2)r_]}{r_+^2(1+\rho^2)^2}[/tex]. Now, the solutions say that this is equal to [tex]\frac{r_+\rho^2(r_+r_)}{r_+^2}\cdot [1+O(\rho^2)] [/tex], however I cannot, for the life of me, see how to get this from my line above! Can anyone help? 


#2
May1307, 07:50 AM

Emeritus
Sci Advisor
PF Gold
P: 9,781

Looks like a Taylor expansion to me, but I could be wrong...



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