  In gamma-ray astronomy through Imaging Atmospheric Cherenkov Telescopes
(IACT), the atmosphere is used as a calorimeter. Incident gamma-rays in the
GeV-TeV energy range are observed through the electromagnetic showers they
produce in the atmosphere and the Cherenkov light emitted by them. We aim to
obtain a parameterisation of the longitudinal profiles of electromagnetic
showers in the atmosphere. The longitudinal Cherenkov emission profiles of
these showers can be used for the reconstruction of the parameters of the
gamma-photon as well gamma-hadron discrimination. Obtaining an accurate
parameterisation of these profiles can therefore be used in the analysis of
IACT images as well as fast simulation of the Cherenkov emission from
gamma-induced showers in the atmosphere. Such parameterisations are not known
to have been systematically carried out prior to this. We carry out Monte Carlo
simulations of gamma-induced showers in the atmosphere. The parameterisation of
their Cherenkov emission longitudinal profiles is based on the well-known
gamma-function used in particle detector physics. We evaluate the dependence of
the depth of the maximum and the average depth of the longitudinal Cherenkov
emission profile, as well as the parameter $1/\beta$ on the energy of the
initial shower. We also study the distributions of various parameters
associated with the gamma-function and find that $\beta/\alpha$ and $1/\alpha$
have Gaussian distributions and are not correlated with each other which makes
them appropriate variables for evaluating the fluctuations of the Cherenkov
emission profiles. We finally present parameterisations of the fluctuations of
these two variables.
