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Abstract: We generalize techniques of Addison to a vastly larger context. We obtainintegral representations in terms of the first periodic Bernoulli polynomialfor a number of important special functions including the Lerch zeta,polylogarithm, Dirichlet $L$- and Clausen functions. These results then enablea variety of Addison-type series representations of functions. Moreover, weobtain integral and Addison-type series for a variety of mathematicalconstants.



Author: Mark W. Coffey

Source: https://arxiv.org/







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