  Context. There are typically two different approaches to inferring the mass
formation history (MFH) of a given galaxy from its luminosity in different
bands. Non-parametric methods are known for their flexibility and accuracy,
while parametric models are more computationally efficient. Aims. In this work
we propose an alternative, based on a polynomial expansion around the present
time, that combines the advantages of both techniques. Methods. In our
approach, the MFH is decomposed through an orthonormal basis of N polynomials
in lookback time. To test the proposed framework, synthetic observations are
generated from models based on common analytical approximations (exponential,
delayed-$\tau$, and Gaussian star formation histories), as well as cosmological
simulations for the Illustris-TNG suite. A normalized distance is used to
measure the quality of the fit, and the input MFH is compared with the
polynomial reconstructions both at the present time and through cosmic
evolution. Our polynomial expansion is also compared with widely used
parametric and non-parametric methods such as CIGALE anda PROSPECTOR. Results.
The observed luminosities are reproduced with an accuracy of around 10 per cent
for a constant star formation rate (N=1) and better for higher-order
polynomials. Our method provides good results on the reconstruction of the
total stellar mass, the star formation rate, and even its first derivative for
smooth star formation histories, but it has difficulties in reproducing
variations on short timescales and/or star formation histories that peak at the
earliest times of the Universe. Conclusions. The polynomial expansion appears
to be a promising alternative to other analytical functions used in parametric
methods, combining both speed and flexibility.
