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Sums of products of Apostol–Bernoulli numbers

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, South Korea

    Min-Soo Kim & Su Hu

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  1. Min-Soo Kim
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  2. Su Hu
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Correspondence to Su Hu.

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Kim, MS., Hu, S. Sums of products of Apostol–Bernoulli numbers. Ramanujan J 28, 113–123 (2012). https://doi.org/10.1007/s11139-011-9340-z

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  • DOI: https://doi.org/10.1007/s11139-011-9340-z

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