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

2010/06/13 by Mark W. Coffey, Coffey, Mark W.
Mathematics · Physics and Astronomy · #11M06 #11M35 #11Y60 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:11M06 #msc:11M35 #msc:11Y60

paper · pdf · doi:10.48550/arxiv.1006.2551

36 pages, no figures

arxiv created 2010/06/13 · arxiv updated 2010/06/15

Abstract

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.

Related

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• Notes on a paper of Tyagi and Holm: A new integral representation for the Riemann Zeta function