Polylogarithms, hyperfunctions and generalized Lipschitz summation formulae

2007/12/06 by Stefano Marmi, Marmi, Stefano, Piergiulio Tempesta +1
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.CV #math.MP #math.NT

paper · pdf · doi:10.48550/arxiv.0712.1046

15 pages

arxiv created 2007/12/06 · arxiv updated 2009/12/01

Abstract

A generalization 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 families of one--dimensional hyperfunctions are also constructed.

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