On the apostol-bernoulli polynomials

Qiu-Ming Luo

Open Mathematics (2004)

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

Abstract

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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.

How to cite

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Qiu-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

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  1. [1] T.M. Apostol: “On the Lerch Zeta function”, Pacific J. Math., Vol. 1, (1951), pp. 161–167. Zbl0043.07103
  2. [2] T.M. Apostol: Introduction to analytic number theory, Springer-Verlag, New York/Heidelberg/Berlin, 1976. 
  3. [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. [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. [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. [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. [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. [8] Qiu-Ming Luo: “The Bernoulli Polynomials Involving the Gaussian Hypergeometric Functions”, [submitted]. 
  9. [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. [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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