International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 629619 | https://doi.org/10.1155/S0161171203112070

Qiu-Ming Luo, Bai-Ni Guo, Feng Qi, Lokenath Debnath, "Generalizations of Bernoulli numbers and polynomials", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 629619, 8 pages, 2003. https://doi.org/10.1155/S0161171203112070

Generalizations of Bernoulli numbers and polynomials

Received03 Dec 2001

Abstract

The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a,b) are generalized to the one Bn(x;a,b,c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a,b), and Bn(x;a,b,c) are established.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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