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Remarks on some relationships between the Bernoulli and Euler polynomials. (English) Zbl 1070.33012
Recently, 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 H. M. Srivastava and J. Choi [Series associated with the zeta and related functions. Dordrecht etc.: Kluwer Academic Publishers (2001; Zbl 1014.33001)] and a paper by H. M. Srivastava, J.-L. Lavoie and R. Tremblay [Can. Math. Bull. 26, 438–445 (1983; Zbl 0504.33007)].

MSC:
11B68 Bernoulli and Euler numbers and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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[1] Cheon, G.-S, A note on the Bernoulli and Euler polynomials, Appl. math. lett., 16, 3, 365-368, (2003) · Zbl 1055.11016
[2] Erdélyi, A; Magnus, W; Oberhettinger, F; Tricomi, F.G, ()
[3] Abramowitz, M; Stegun, I.A, ()
[4] Magnus, W; Oberhettinger, F; Soni, R.P, ()
[5] Hansen, E.R, ()
[6] Srivastava, H.M; Choi, J, ()
[7] Erdélyi, A; Magnus, W; Oberhettinger, F; Tricomi, F.G, ()
[8] Luke, Y.L, ()
[9] Srivastava, H.M; Lavoie, J.-L; Tremblay, R, A class of addition theorems, Canad. math. bull., 26, 438-445, (1983) · Zbl 0504.33007
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