Gaisser–Hillas function
The Gaisser–Hillas function is used in astroparticle physics. It parameterizes the longitudinal particle density in a cosmic ray air shower. The function was proposed in 1977 by Thomas K. Gaisser and Anthony Michael Hillas. The number of particles  as a function of traversed atmospheric depth  is expressed as

where  is maximum number of particles observed at depth , and  and  are primary mass and energy dependent parameters. Using substitutions

,    and  

the function can be written in an alternative one-parametric (m) form as

References 

Cosmic rays