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In the study of periodic media, conditionally convergent series arefrequently encountered and their regularization is crucial for applications. Wederive an identity that regularizes two-dimensional generalized Eisensteinseries for all Bravais lattices, yielding physically meaningful values. We alsoobtain explicit forms for the generalized series in terms of conventionalEisenstein series, enabling their closed-form evaluation for important highsymmetry lattices. Results are then used to obtain representations for therelated cylindrical harmonic sums, which are also given for all Bravaislattices. Finally, we treat displaced lattices of high symmetry, expressingthem in terms of origin-centered lattices via geometric multi-set identities.These identities apply to all classes of two-dimensional sums, allowing sums tobe evaluated over each constituent of a unit cell that possesses multipleinclusions.

Evaluation and regularization of generalized Eisenstein series and application to 2D cylindrical harmonic sums