Given this equation:

$$ \frac{1}{r}\frac{d}{dr}\bigg(r \frac{dT}{dr} \bigg) - \bigg(\frac{2h}{bk} \bigg)(T-T_a) = 0 $$

I can let $x=r\sqrt{(2h/bk)}$ and $z=T-T_a$ to obtain the bessel equation using the appropriate substitutions

$$ x^2 \frac{d^2z}{dx^2} + x \frac{dz}{dx} - x^2z = 0 $$

To express the solution for $z$, I read that one technique is to use the Frobenius method, but I am not sure how to apply this to be Bessel function above... Any help ?


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