t_1 = t_0 + \Delta

t_1' = \min \{ t \ge t_1 \mid W(\mathrm{dow}(t))=1,\ \mathrm{date}(t)\notin\mathcal{H},\ \mathrm{time}(t)\in[\tau_s,\tau_e] \}

t_{\text{start}} = t_1' - b_{\text{before}}, \qquad t_{\text{end}} = t_1' + d + b_{\text{after}}

t_{k} = t_{\text{start}} + k \cdot \phi,\quad u_{k} = t_{\text{end}} + k \cdot \phi

Offset addition: Let \( t_0 \) be the start datetime, \( \Delta \) the offset, and \( \phi \) the recurrence step. The single appointment start is: \[ t_1 = t_0 + \Delta \] If business days only is enabled with working-day indicator \( W(d) \in \{0,1\} \) and holiday set \( \mathcal{H} \), advance day-by-day until conditions meet: \[ t_1' = \min \{ t \ge t_1 \mid W(\mathrm{dow}(t))=1,\ \mathrm{date}(t)\notin\mathcal{H},\ \mathrm{time}(t)\in[\tau_s,\tau_e] \} \] Buffers and duration: \[ t_{\text{start}} = t_1' - b_{\text{before}}, \qquad t_{\text{end}} = t_1' + d + b_{\text{after}} \] Recurrence for occurrence \( k=0,\dots,n-1 \): \[ t_{k} = t_{\text{start}} + k \cdot \phi,\quad u_{k} = t_{\text{end}} + k \cdot \phi \]