$$ SARIMA \left\{ (p,d,q) \times (P,D,Q)_m \right\} $$
$$ \Delta_mY_t=Y_t-Y_{t-m} $$
$$ Y_t=c+\sum_{n=1}^{p}\beta_nY_{t-n}+\sum_{n=1}^{q}\theta_n\varepsilon_{t-n}+\sum_{n=1}^{P}\phi_nY_{t-sn}+\sum_{n=1}^{Q}\eta_n\varepsilon_{t-sn}+\varepsilon_t $$
$$ Y_t=c+\sum_{n=1}^{p}\beta_nY_{t-n}+\sum_{n=1}^{q}\theta_n\varepsilon_{t-n}+ \sum_{n=1}^r\beta_n x_{n_t} +\sum_{n=1}^{P}\phi_nY_{t-sn}+\sum_{n=1}^{Q}\eta_n\varepsilon_{t-sn}+\varepsilon_t $$