abstract: A new construction relating formal groups, Bernoulli--type polynomials and Dirichlet L-series is proposed. It generalizes the correspondence between the standard Bernoulli polynomials and the Riemann zeta function. By using the Fourier expansion of the Bernoulli--type polynomials, a generalization of the classical Lipschitz summation formula is also proposed. Related families of one--dimensional hyperfunctions are explicitly constructed.