question about ARMA process

[e0ne199]

TL;DR Summary

I want to change arma process into transfer function, I have done it but I am unsure if it is correct or not

hello everyone, I have a question about stochastic process (ARMA process) that looks like this :

I would like to change it into a transfer function, so the final result looks like this :

My question is, is this equation correct? if it is not correct, what should I change for this equation?