General formula for multiplication in polynomial quotient ring

Question

For two polynomials $p$ and $q$, one has that: $$p \cdot q = \left( \sum_{i=0}^{\deg p} p_i x^i\right) \cdot \left( \sum_{j=0}^{\deg q} q_j x^j\right) = \sum_{k=0}^{\deg p + \deg q} \sum_{l=0}^k p_l q_{k-l} x^k$$ Now assume we are instead working in the quotient ring $R[X]/(X^n+1)$, so our multiplication is module $X^n+1$. Can such a general formula for a multiplication for two polynomials $p, \cdot q \mod (X^n +1)$, where $p, q \in R[x]/(X^n+1)$ be obtained?