  The Voigt-Hjerting function is fundamental in order to correctly model the
profiles of absorption lines imprinted in the spectra of bright background
sources by intervening absorbing systems. In this work we present a simple
analytic approximation to this function in the context of absorption line
profiles of intergalactic HI absorbers. Using basic calculus tools, we derive
an analytic expression for the Voigt-Hjerting function that contains only
fourth order polynomial and Gaussian functions. In connection with the
absorption coefficient of intergalactic neutral hydrogen, this approximation is
suitable for modeling Voigt profiles with an accuracy of $10^{-4}$ or better
for an arbitrary wavelength baseline, for column densities up to $N_{HI} =
10^{22} cm^{-2}$, and for damping parameters $a \lesssim 10^{-4}$, i.e. the
entire range of parameters characteristic to all Lyman transitions arising in a
variety of HI absorbing systems such as Lyman Alpha Forest clouds, Lyman Limit
systems and Damped Lyman Alpha systems. We hence present an approximation to
the Voigt-Hjerting function that is both accurate and flexible to implement in
various types of programming languages and machines, and with which Voigt
profiles can be calculated in a reliable and very simple manner.
