  The Shannon and the Renyi entropies of the ground state wavefunction in the
pure and in the random quantum Ising chain are studied via the self-dual
Fernandez-Pacheco real-space renormalization procedure. In particular, we
analyze the critical behavior of the leading extensive term at the quantum
phase transition : the derivative with respect to the control parameter is
found to be logarithmically divergent in the pure case, and to display a cusp
singularity in the random case. This cusp singularity for the random case is
also derived via the Strong Disorder Renormalization approach.
