Triple convolution identities on Bernoulli polynomials and Euler polynomials

Abstract

In this paper, by means of the generating function method, we establish 38 triple convolution identities on the Bernoulli polynomials and the Euler polynomials (i.e., sums of products of three Bernoulli polynomials or Euler polynomials), which have the form (Equation presented) where α, β, γ ∈ ℕ₀, λ,μ ∈ ℂ, and F_k(x),G_k(y),H_k(z) are the Bernoulli polynomials or the Euler polynomials. As supplements, we also give 3 quadruple convolution identities on the Bernoulli and Euler polynomials and 4 triple convolution identities on the Bernoulli and Euler numbers.