Rendiconti del Circolo Matematico di Palermo

, Volume 56, Issue 1, pp 43–56 | Cite as

Jackson’s integral of the Hurwitz zeta function

  • Nobushige Kurokawa
  • Katsuhisa Mimachi
  • Masato Wakayama
Article

Abstract

We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function.

2000 Mathematics Subject Classification

11M36 

Key Words

Hurwitz’s zeta Jackson’s integral Lerch’s formula Raabe’s integral formula double sine function 

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Copyright information

© Springer 2007

Authors and Affiliations

  • Nobushige Kurokawa
    • 1
  • Katsuhisa Mimachi
    • 2
  • Masato Wakayama
    • 3
  1. 1.Department of Mathematics Tokyo Institute of TechnologyOh-okayama MeguroTokyoJapan
  2. 2.Department of Mathematics Tokyo Institute of TechnologyOh-okayama MeguroTokyoJapan
  3. 3.Faculty of MathematicsKyushu UniversityHakozaki FukuokaJapan

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