# On the apostol-bernoulli polynomials

Open Mathematics (2004)

- Volume: 2, Issue: 4, page 509-515
- ISSN: 2391-5455

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topQiu-Ming Luo. "On the apostol-bernoulli polynomials." Open Mathematics 2.4 (2004): 509-515. <http://eudml.org/doc/268768>.

@article{Qiu2004,

abstract = {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.},

author = {Qiu-Ming Luo},

journal = {Open Mathematics},

keywords = {Primary: 11B68; Secondary: 33C05, 11M35, 30E20},

language = {eng},

number = {4},

pages = {509-515},

title = {On the apostol-bernoulli polynomials},

url = {http://eudml.org/doc/268768},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Qiu-Ming Luo

TI - On the apostol-bernoulli polynomials

JO - Open Mathematics

PY - 2004

VL - 2

IS - 4

SP - 509

EP - 515

AB - 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.

LA - eng

KW - Primary: 11B68; Secondary: 33C05, 11M35, 30E20

UR - http://eudml.org/doc/268768

ER -

## References

top- [1] T.M. Apostol: “On the Lerch Zeta function”, Pacific J. Math., Vol. 1, (1951), pp. 161–167. Zbl0043.07103
- [2] T.M. Apostol: Introduction to analytic number theory, Springer-Verlag, New York/Heidelberg/Berlin, 1976.
- [3] L. Comtet: Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht/Boston, 1974. (Translated from the French by J.W. Nienhuys) Zbl0283.05001
- [4] H.M. Srivastava: “Some formulae for the Bernoulli and Euler polynomials at rational arguments”, Math. Proc. Cambridge Philos. Soc., Vol. 129, (2000), pp. 77–84. http://dx.doi.org/10.1017/S0305004100004412 Zbl0978.11004
- [5] H.M. Srivastava and Junesang Choi: Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2001. Zbl1014.33001
- [6] H.M. Srivastava, P.G. Todorov: “An explicit formula for the generalized Bernoulli polynomials”, J. Math. Anal. Appl., Vol. 130, (1988), pp. 509–513. http://dx.doi.org/10.1016/0022-247X(88)90326-5
- [7] H.W. Gould: “Explicit formulas for Bernoulli numbers” Amer. Math. Monthly, Vol. 79, (1972), pp. 44–51. http://dx.doi.org/10.2307/2978125 Zbl0227.10010
- [8] Qiu-Ming Luo: “The Bernoulli Polynomials Involving the Gaussian Hypergeometric Functions”, [submitted].
- [9] D. Cvijovic and J. Klinowski: “New formula for The Bernoulli and Euler polynomials at rational arguments”, Proc. Amer. Math. Soc., Vol. 123, (1995), pp. 1527–1535. http://dx.doi.org/10.2307/2161144 Zbl0827.11012
- [10] M. Abramowitz and I.A. Stegun (Eds): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 4th printing, Washington, 1965.

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