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# van der Pol Expansions of L-Series

Published:2007-03-01
Printed: Mar 2007
• David Borwein
• Jonathan Borwein
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## Abstract

We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.
 Keywords: Dirichlet series integrals, Hurwitz zeta functions, Plancherel theorems, L-series
 MSC Classifications: 11M35 - Hurwitz and Lerch zeta functions 11M41 - Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 30B50 - Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]