  This paper provides, firstly, a succinct mathematical derivation of
Bose-Einstein condensation (BEC) of photons elaborating on previous results
[M\"uller, E.E., Annals of Phys. 184, 219-230 (1988); M\"uller, E.E. Physica
139A, 165-174 (1986)] including new results on the condensate function, and,
secondly, applies this framework to consistently explain experimental findings
reported in Klaers J., Schmitt, J., Vewinger, F & Weitz, M., Nature 468,
545-548 (2010). The theoretical approach presented here invites to
significantly widen the experimental framework for BEC of photons including
three-dimensional photon resonators and thermalization mechanisms different
from a dye medium in the cavity.
