There exists four $\beta$ and $\gamma$ coefficients for a distribution that describe the shape of a distribution. I know the relation between $\beta_1 $ and $\gamma_1 $ which is $\gamma_1 = \sqrt \beta_1$ and similarly $\gamma_2 = \beta_2 - 3$.
But is there any other relation between $\beta_1$ and $\beta_2$ or a relation between $\gamma_1$ and $\gamma_2$?
I tried searching but I couldn't find anything. Sorry if I am asking something very obvious, maybe I am just a noob.