  We obtain a generalization of the Burns-Krantz rigidity theorem for
holomorphic self-mappings of the unit disk in the spirit of the classical
Schwarz-Pick Lemma and its continuous version due to L.Harris via the
generation theory for one-parameter semigroups. In particular, we establish
geometric and analytic criteria for a holomorphic function on the disk with a
boundary null point to be a generator of a semigroup of linear fractional
transformations under some relations between three boundary derivatives of the
function at this point.
