I am trying to understand the basics of Renormalization. I have read that β encodes the running coupling and can be expanded as a power series as: β(g) = ∂g/(∂ln(μ)) = β0g3 + β1g5 + ... However, I don't understand how this is derived.. I assume that the terms correspond to 1 loop, 2 loops etc. Can somebody help me out.