An analytical representation of the mass-energy threshold of a Photon is derived utilising finite reciprocal harmonics. The derived value is "<5.75 x 10-17 (eV)" and is within 4.3(%) of the Eidelman et. al. value endorsed by the Particle Data Group (PDG) "< 6 x 10-17 (eV)". The PDG value is an adjustment of theoretical predictions to fit physical observation. The derivation presented herein is without adjustment and may represent physical evidence of the existence of Euler's Constant in nature at the quantum level.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.