  We consider the linearized electrical impedance tomography problem in two
dimensions on the unit disk. By a linearization around constant coefficients
and using a trigonometric basis, we calculate the linearized
Dirichlet-to-Neumann operator in terms of moments of the conduction coefficient
of the problem. By expanding this coefficient into angular trigonometric
functions and Legendre-M\"untz polynomials in radial coordinates, we can find a
lower-triangular representation of the parameter to data mapping. As a
consequence, we find an explicit solution formula for the corresponding inverse
problem. Furthermore, we also consider the problem with boundary data given
only on parts of the boundary while setting homogeneous Dirichlet values on the
rest. We show that the conduction coefficient is uniquely determined from
incomplete data of the linearized Dirichlet-to-Neumann operator with an
explicit solution formula provided.
