Abstract:
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.