The Euler-Maclaurin formula states an interdependency between

\begin{align} I\quad:=&&\int_m^nf(x)dx;\ m,n\in\mathbb{Z}\\ S\quad:=&&\sum_{k=m}^{n}{f(k)}\\ D\quad:=&&\lbrace \frac{d^j}{dx^j}f(m)\rbrace\cup\lbrace \frac{d^j}{dx^j}f(n)\rbrace \end{align}

The Euler-Maclauring formula is "traditionally" used to estimate the value of $S$ from $I$ and $D$ and also to estimate $I$ from $S$ and $D$

Question:

are there examples where the Euler-Maclaurin formula has been beneficially used to fix the the values of the derivatives of a function in the endpoints of its integration interval in order to fix the values of the elements of $D$ via $\lbrace I,\left(x_i,y_i\right)_{i=m}^{n}\rbrace$?

To be specific: have there been attempts to determine the values of the elements of $D$ via the Euler-Maclaurin formula to find "ideal" derivatives for use in clamped spline-interpolation, i.e. where the disambiguation of the interpolation is done via fixing derivatives at the ends of the interpolation interval by plugging the (estimated) value of $I$ and/or the coordinate values of the $\left(x_i,f(x_i)\right)$ into the Euler-Maclaurin formula?