Integral representations of functions and Addison-type series for mathematical constants

Details Integral representations of functions and Addison-type series for mathematical constants Integral representations of functions and Addison-type series for mathematical constants

2010-06-13

arxiv.org/abs/1006.2551v1

Physics

Mathematical Physics

36 pages, no figures

Scientific paper

We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm, Dirichlet $L$- and Clausen functions. These results then enable a variety of Addison-type series representations of functions. Moreover, we obtain integral and Addison-type series for a variety of mathematical constants.

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