Sums of products of Apostol–Bernoulli numbers
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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.
KeywordsSums of products Multiple Hurwitz–Lerch zeta functions Apostol–Bernoulli numbers and polynomials
Mathematics Subject Classification (2000)11M35 11B68
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