Abstract
We describe with some new details the connection between generalized Bernoulli polynomials, Bernoulli polynomials and generalized Bernoulli numbers (Norlund polynomials). A new recursive and explicit formulae for these polynomials are derived.
Similar content being viewed by others
References
Bretti, G., Natalini, P., Ricci, P.E.: Generalizations of the Bernoulli and Appel polynomials. Abstract Appl. Anal. 7, 613–623 (2004). doi:10.1155/S1085337504306263
Burić T., Elezović N.: Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions. J. Comput. Appl. Math. 235, 3315–3331 (2011)
Chen C.-P., Elezović N., Vukšić L.: Asymptotic formulae associated with the Wallis power function and digamma function. J. Class. Anal. 2(2), 151–166 (2013)
Dilcher K.: Sums of products of Bernoulli numbers. J. Number Theory 60(1), 23–41 (1996)
Gessel I.M.: On Mikis identity for Bernoulli numbers. J. Number Theory 110, 75–82 (2005)
Kim M.-S.: A note on sums of products of Bernoulli numbers. Appl. Math. Lett. 24(1), 55–61 (2011)
Lu D.-Q.: Some properties of Bernoulli polynomials and their generalizations. Appl. Math. Lett. 24, 746–751 (2011)
Luke, Y.L.: The Special Functions and Their Approximations, Vol. I. Academic Press, New York (1969)
Natalini, P., Bernardini, A.: Generalization of the Berboulli polynomials. J. Appl. Math. 3, 155–163 (2003). doi:10.1155/S1110757X03203101
Srivastava H.M., Pintér Á.: Remarks on some relationships between the Bernoulli and Euler polynomials. Appl. Math. Lett. 17, 375–380 (2004)
Tempesta P.: On Appell sequences of polynomials of Bernoulli and Euler type. J. Math. Anal. Appl. 341, 1295–1310 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by Croatian Science Foundation under the project 5435.
Rights and permissions
About this article
Cite this article
Elezović, N. Generalized Bernoulli Polynomials and Numbers, Revisited. Mediterr. J. Math. 13, 141–151 (2016). https://doi.org/10.1007/s00009-014-0498-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-014-0498-7