The Akiyama-Tanigawa algorithm for Bernoulli numbers.

Kaneko, Masanobu

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On the apostol-bernoulli polynomials

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In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.