Buildup factors for various shielding materials exhibit large variations in magnitude and in curve shapes as a function of penetration depth as a result of the stochastic nature of the scattering processes for different incident photon energies. In a quest for adequate functional representation of point isotropic gamma-ray buildup factor data, a family of functions based on an expanded polynomial orthogonal set is introduced.The approximation function has the form .In the foregoing formula, a and β are generally constants that differ for each material, and in that respect, this formula presents a family of functions, while Ai are independent parameters of the function. This is not always valid, and for some materials, modifications are introduced where besides Ai, an additional independent parameter is (β while a remains constant throughout the whole energy domain.A polynomial-based function approach is validated as a possible choice [besides the well-known geometrical-progression (G-P) function] for point-kernel calculations. Results of approximations to exposure point isotropic buildup factors for water, concrete, and iron with four and for lead and beryllium with five independent parameters of presented function are in good agreement with the basic data within 4%, over the standard data domain. The results are compared with five-parameter G-P function fitting on the maximum-percentage-relative-error basis. The validity of using the independent parameters of the function to interpolate buildup factors for intermediate source energies is ascertained.