  Computational challenges associated with the use of Wigner functions to
identify non-classical properties of states are addressed with the aid of
generating functions. It allows the computation of the Wigner functions of
photon-subtracted states for an arbitrary number of subtracted photons. Both
the formal definition of photon-subtracted states in terms of ladder operators
and the experimental implementation with heralded photon detections are
analyzed. These techniques are demonstrated by considering photon subtraction
from squeezed thermal states as well as squeezed Fock states. Generating
functions are also used for the photon statistics of these states. These
techniques reveal various aspects of the parameter dependences of these states.
