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.
@article{bwmeta1.element.doi-10_2478_BF02475959,
author = {Qiu-Ming Luo},
title = {On the apostol-bernoulli polynomials},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {509-515},
zbl = {1073.33001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475959}
}
Qiu-Ming Luo. On the apostol-bernoulli polynomials. Open Mathematics, Tome 2 (2004) pp. 509-515. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475959/
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