  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.
