  In this article we prove that if the coefficients of a Fourier-Legendre
expansion satisfy a suitable Hausdorff-type condition, then the series
converges to a function which admits a holomorphic extension to a cut-plane.
Furthermore, we prove that a Laplace-type (Laplace composed with Radon)
transform of the function describing the jump across the cut is the unique
Carlsonian interpolation of the Fourier coefficients of the expansion. We can
thus reconstruct the discontinuity function from the coefficients of the
Fourier-Legendre series by the use of the Pollaczek polynomials.
