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New Characterization of Appell polynomials

Research paper by Abdelmejid Bayad, Takao Komatsu

Indexed on: 24 Jul '16Published on: 24 Jul '16Published in: Mathematics - Number Theory



Abstract

We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In addition, from our study, we obtain Fourier expansions of Appell polynomials. This result recovers Fourier expansions known for Bernoulli and Euler polynomials and obtains the Fourier expansions for higher order Bernoulli-Euler's one.