  We prove the null controllability of a one dimensional degenerate parabolic
equation with drift and a singular potential. We study the case the potential
arises at the left end point and the weighted Dirichlet boundary control is
located at this point. We get a spectral decomposition of a suitable operator,
defined in a weighted Sobolev space, involving Bessel functions and their
zeros, then we use the moment method by Fattorini and Russell to obtain an
upper estimate of the cost of controllability. We also obtain a lower estimate
of the cost of controllability by using a representation theorem for analytic
functions of exponential type.
