On the apostol-bernoulli polynomials

• Autorzy: Qiu-Ming Luo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bernoulli numbers; Bernoulli polynomials; Apostol-Bernoulli numbers; Apostol-Bernoulli polynomials; Gaussian hypergeometric functions; Stirling numbers of the second kind; Hurwitz Zeta functions; Lerch functional equation; Primary: 11B68; Secondary: 33C05, 11M35, 30E20

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 4
• Strony: 509-515

Daty

wydano

2004-08-01

online

2004-08-01

Twórcy

autor

Qiu-Ming Luo

• Jiaozuo University

Bibliografia

• [1] T.M. Apostol: “On the Lerch Zeta function”, Pacific J. Math., Vol. 1, (1951), pp. 161–167.
• [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)
• [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
• [5] H.M. Srivastava and Junesang Choi: Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2001.
• [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
• [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
• [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.

Identyfikatory

DOI

10.2478/BF02475959