Polylogarithms, hyperfunctions and generalized Lipschitz summation formulae
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🧮 math.NT
math-phmath.CVmath.MP
keywords
constructedhyperfunctionslipschitzsummationbernoulli--typecertainclassicalexpansion
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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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