Wang Xiaoying and Zhang Wenpeng: Several new identities involving Euler and Bernoulli polynomials, p.101-108


The main purpose of this paper is using the elementary and combinational methods to obtain several new identities for Euler and Bernoulli polynomials. As some applications of these identities, we give several interesting relationships between these polynomials and some famous sequences (such as Fibonacci sequences and Lucas sequences) or numbers (such as Mersenne numbers and Fermat numbers).

Key Words: Euler polynomials; Bernoulli polynomials; identity; Fibonacci sequences; Lucas sequences; Pell sequences; Mersenne numbers; Fermat numbers.

2000 Mathematics Subject Classification: Primary: 11B37;
Secondary: 11B83.