  We present a general framework for calculating the Volterra-type convolution
of polynomials from an arbitrary polynomial sequence $\{P_k(x)\}_{k \geqslant
0}$ with $\deg P_k(x) = k$. Based on this framework, series representations for
the convolutions of classical orthogonal polynomials, including Jacobi and
Laguerre families, are derived, along with some relevant results pertaining to
these new formulas.
