We present a detailed measurement of charged two-pion correlation functions in 0%-30% centrality √ s N N = 200 GeV Au+Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from Lévy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter λ, the Lévy index of stability α and the Lévy length scale parameter R as a function of average transverse mass of the pair mT . We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same Lévy-stable source functions. The λ(mT ) measurements indicate a decrease of the strength of the correlations at low mT . The Lévy length scale parameter R(mT ) decreases with increasing mT , following a hydrodynamically predicted type of scaling behavior. The values of the Lévy index of stability α are found to be significantly lower than the Gaussian case of α = 2, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.