Mathematica Solve equation perturbatively

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To solve the expression T = 2 P r - (q^2 / (4 π r^3)) + (1 / (4 π r)) for r perturbatively, the discussion emphasizes the need to identify a small parameter for the perturbation expansion. The derived expression for r is r = (T / (2 P)) - (1 / (4 π T)) + (P (8 π P q^2 - 1)) / (8 (π^2 T^3)) + ..., indicating a series expansion around a specific value of r. The conversation also seeks guidance on implementing this perturbative solution in Mathematica, highlighting the importance of clearly defining the small parameter to facilitate the computation. The focus is on practical steps for executing the perturbative method within the software.
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I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading an article where author did this. How can I do this in mathematica?
 
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Which is your small parameter? It is unclear from your post.
 
djymndl07 said:
How can I do this in mathematica?
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