  The deflection, potential, shear and magnification of a gravitational lens
following an elliptical power law mass model are investigated. This mass model
is derived from the circular power law profile through a rescaling of the axes,
similar to the case of a singular isothermal ellipsoid. The resulting
deflection can be calculated explicitly and given in terms of the Gaussian
hypergeometric function. Analytic expressions for the remaining lensing
properties are found as well. Because the power law profile lens contains a
number of well-known lens models as special cases, the equivalence of the new
expressions with known results is checked. Finally, it is shown how these
results naturally lead to a fast and accurate numerical scheme for computing
the deflection and other lens quantities, making this method a useful tool for
realistically modelling observed lenses.
