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In this paper, we give an integral representation for the boundary values ofderivatives 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 resultof Ahern--Clark obtained for functions of the model spaces $K_b$, where $b$ isan inner function. Using hypergeometric series, we obtain a nontrivial formulaof combinatorics for sums of binomial coefficients. Then we apply this formulato show the norm convergence of reproducing kernel $k_{\omega,n}^b$ of theevaluation of $n$-th derivative of elements of $\HH(b)$ at the point $\omega$as it tends radially to a point of the real axis.

Integral representation of the $n$-th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel