Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials

Abstract

In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, and present several new recurrence relations for the Bernoulli numbers and polynomials.

Keywords

• determinantal expression
• recurrence relation
• Bernoulli number
• Bernoulli polynomial
• Hessenberg determinant