Since its invention, the phasor has essentially been considered as a steady-state concept. Up to now, this assumption has shaped most of the algorithms for phasor estimation. This paper breaks that old paradigm by relaxing the static phasor concept to a dynamic one, i.e., the dynamic phasor, which is one complex time function with movement freedom. This paper presents the algorithm to approximate the dynamic phasor by a second-order Taylor polynomial and compares its phasor estimate to the traditional one. This approximation leads to the definition of the phasor state vector, which contains not only the estimate of the dynamic phasor but the estimates of its derivatives as well. These new estimates improve the accuracy of oscillation estimation by including new Taylor details into the interpolation process. Errors on the order of 10-4 are achieved with this approximation in bandpass signals over observation intervals of two cycles.