In this paper the main result (Theorem 2) gives the following formula for the Bernoulli polynomials
where is a complex number, and are integers, and
Furthermore the author derives (Theorem 1) twelve formulas for the Bernoulli and Euler numbers and the Bernoulli and Euler polynomials, e.g.
The proofs make use of the combinatorial identity of H. W. Gould [Combinatorial identities (1972; Zbl 0241.05011)]
and the formulas of H. Alzer [Mitt. Math. Ges. Hamb. 11, 469-471 (1987; Zbl 0632.10008)] and K. Dilcher [Abh. Semin. Univ. Hamb. 59, 143- 156 (1989; Zbl 0712.11015)] for the Bernoulli and Euler polynomials.