  In this paper, we give an integral representation for the boundary values of
derivatives of functions of the de Branges--Rovnyak spaces $\HH(b)$, where $b$
is in the unit ball of $H^\infty(\CC_+)$. In particular, we generalize a result
of Ahern--Clark obtained for functions of the model spaces $K_b$, where $b$ is
an inner function. Using hypergeometric series, we obtain a nontrivial formula
of combinatorics for sums of binomial coefficients. Then we apply this formula
to show the norm convergence of reproducing kernel $k_{\omega,n}^b$ of the
evaluation of $n$-th derivative of elements of $\HH(b)$ at the point $\omega$
as it tends radially to a point of the real axis.
