Highly Influenced

# Identities concerning Bernoulli and Euler polynomials by

@inproceedings{Sun2004IdentitiesCB, title={Identities concerning Bernoulli and Euler polynomials by}, author={Zhi-Wei Sun}, year={2004} }

- Published 2004

Clearly Bn(0) = Bn and En(1/2) = En/2 . Here are some basic properties of the Bernoulli and Euler polynomials we will need later: Bn(1− x) = (−1) Bn(x), ∆(Bn(x)) = nx , En(1− x) = (−1) En(x), ∆ (En(x)) = 2x . Here, the operators ∆ and ∆ are defined by ∆(f(x)) = f(x+1)−f(x) and ∆(f(x)) = f(x+ 1) + f(x). It is also known that B n+1(x) = (n+ 1)Bn(x) and E n+1(x) = (n+ 1)En(x). For a sequence {an}n∈N of complex numbers, its dual sequence {a ∗ n}n∈N is given by an = ∑n k=0 ( n k )