I have a question about the transformation of pdf.
$f(y|x)\propto\frac{\Gamma(\alpha+\frac{1}{2})}{[\frac{1}{2}(y-\mu)^2+\beta]^{(\alpha+\frac{1}{2})}}\propto[\frac{(y-\mu)^2}{2\beta}+1]^{-(\alpha+\frac{1}{2})}$
Does anyone could help me on how the right-hand side of the equation comes from the left-hand side of equation?
Thank you very much!