Integral representations of functions and Addison-type series for mathematical constants
| Autor: | Mark W. Coffey |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Algebra and Number Theory
Polylogarithm Series (mathematics) Mathematics::Number Theory Stieltjes constants FOS: Physical sciences Mathematical Physics (math-ph) Hurwitz zeta function Algebra Lerch zeta function Special functions 11M06 11Y60 11M35 Mathematical constant Glaisher–Kinkelin constant Mathematical Physics Mathematics |
| Zdroj: | Journal of Number Theory. 157:79-98 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2015.04.005 |
| Popis: | 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. 36 pages, no figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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