  We generalise the notion of the Pseudo-Laplacian on a hyperbolic Riemann
surface with one cusp, that was studied by Lax and Phillips and Colin de
Verdi\`ere, by considering a boundary condition of Robin type for the constant
term instead of the classical Dirichlet condition. The resulting family of
Pseudo-Laplacians is a holomorphic family of unbounded operators in the sense
of Kato. By use of holomorphic perturbation theory, we study the eigenvalues
and eigenvectors of this family and give a new proof for the meromorphic
continuation of the Eisenstein series.
