Remarks on some relationships between the Bernoulli and Euler polynomials.

*(English)*Zbl 1070.33012Recently, 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)].

Reviewer: H. M. Srivastava (Victoria)

##### MSC:

11B68 | Bernoulli and Euler numbers and polynomials |

33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |

##### 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
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\textit{H. M. Srivastava} and \textit{Á. Pintér}, Appl. Math. Lett. 17, No. 4, 375--380 (2004; Zbl 1070.33012)

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##### References:

[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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