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Zbl 1070.33012
Srivastava, H.M.; Pintér, Á.
Remarks on some relationships between the Bernoulli and Euler polynomials.
(English)
[J] Appl. Math. Lett. 17, No. 4, 375-380 (2004). ISSN 0893-9659

Recently, {\it G.-S. Cheon} [Appl. Math. Lett. 16, No. 3, 365--368 (2003; Zbl 1055.11016)] rederived several known properties and relationships involving the classical Bernoulli and Euler polynomials. The object of the present sequel to Cheon's work is to shown (among other things) that the main relationship (proven by Cheon) can easily be put in a much more general setting. Some analogous relationships between the Bernoulli and Euler polynomials are also considered. Several closely-related earlier works on this subject include (for example) a recent book by {\it H. M. Srivastava} and {\it J. Choi} [Series associated with the zeta and related functions. Dordrecht etc.: Kluwer Academic Publishers (2001; Zbl 1014.33001)] and a paper by {\it H. M. Srivastava, J.-L. Lavoie} and {\it R. Tremblay} [Can. Math. Bull. 26, 438--445 (1983; Zbl 0504.33007)].
[H. M. Srivastava (Victoria)]
MSC 2000:
*11B68 Bernoulli numbers, etc.
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Bernoulli polynomials; Euler polynomials; generating functions; Bernoulli numbers; Euler numbers; addition theorem; multiplication theorem; generalized Bernoulli polynomials and numbers; generalized Euler polynomials and numbers

Citations: Zbl 1055.11016; Zbl 0504.33007; Zbl 1014.33001

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