Hyperfunctions, formal groups and generalized Lipschitz summation formulas

A construction relating the theory of hyperfunctions with the theory of formal groups and generalizations of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli-type polynomials, related to the Lazard formal group. Related families of one-dimensional hyperfunctions are also constructed.