Max and min functions in spherical expansions

[snatchingthepi]

Homework Statement

Finding the vector potential inside and outside of a rotating homogenous solid sphere.

Relevant Equations

$r_< = min(r,r')$
$r_> = max(r,r')$

I'm trying to solve the vector potential of a solid rotating sphere with a constant charge density. I'm at a point where I'm performing the final integral that looks like

$$ -\left( \frac {\mu_0 i} {3} \right) \sqrt{\frac 3 {2\pi}} \frac {q\omega}{R^3} Y_{1,1} \int_0^R (r')^3 \frac {r_<} {r_>^2} dr'$$I'm thinking that outside the sphere $r_> = r$ and $r_< = r'$, and vice-versa for inside the sphere. Is this correct? I've never seen those functions before, and am unsure if I'm interpretating them correctly.

 

[kuruman]

Your interpretation of $r_>$ and $r_<$ is correct. I have not checked the correctness of the the integral.

 

[snatchingthepi]

Not a problem. My concern was with the min and max functions. Thank you.