The Ramanujan Journal

, Volume 28, Issue 1, pp 113–123 | Cite as

Sums of products of Apostol–Bernoulli numbers



By expressing the sums of products of the Apostol–Bernoulli polynomials in terms of the special values of multiple Hurwitz–Lerch zeta functions at non-positive integers, we obtain the sums of products identity for the Apostol–Bernoulli numbers which is an analogue of the classical sums of products identity for Bernoulli numbers dating back to Euler.


Sums of products Multiple Hurwitz–Lerch zeta functions Apostol–Bernoulli numbers and polynomials 

Mathematics Subject Classification (2000)

11M35 11B68 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKorea Advanced Institute of Science and Technology (KAIST)DaejeonSouth Korea

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