Journal of the
Korean Mathematical Society JKMS

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.

Keywords: Bernoulli polynomials, Euler polynomials, convolution sums, divisor functions

MSC numbers: 11B68, 11A05, 11K65