\begin{definition}[Definition:Operator of Integrated Weighted Derivatives]
Let $n \in \N$.
Let $a_i : \closedint a b \to \R$ be Riemann integrable functions.
Let $h \in \CC^n \closedint a b$ be a Riemann integrable real-valued function of differentiability class $n$.
Then the '''operator of integrated weighted derivatives''' is defined as:
:$\ds \map L h := \int_a^b \sum_{i \mathop = 0}^n \map {a_i} t \map {h^{\paren i} } t \rd t$
where $\ds \int_a^b \map f t \rd t$ denotes the Riemann integral, and $h^{\paren i}$ is the $i$-th derivative of $h$.
\end{definition}