  A distinguishing feature of fractional quantum Hall (FQH) states is a
singular behavior of equilibrium densities at boundaries. In contrast to states
at integer filling fraction, such quantum liquids posses an additional dipole
moment localized near edges. It enters observable quantities such as universal
dispersion of edge states and Lorentz shear stress. For a Laughlin state, this
behavior is seen as a peak, or overshoot, in the single particle density near
the edge, reflecting a general tendency of electrons in FQH states to cluster
near edges. We compute the singular edge behavior of the one particle density
by a perturbative expansion carried out around a completely filled Landau
level. This correction is shown to fully capture the dipole moment and the
major features of the overshoot observed numerically. Furthermore, it exhibits
the Stokes phenomenon with the Stokes line at the boundary of the droplet,
decaying like a Gaussian inside and outside the liquid with different decay
lengths. In the limit of vanishing magnetic length the shape the overshoot is a
singular double layer with a capacity that is a universal function of the
filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH
states. The result suggests an explicit connection between the magnitude of the
dipole moment and the bulk odd viscosity.
