Integral representations of the Legendre chi function

We, by making use of elementary arguments, deduce integral representations of the Legendre chi function χs (z) valid for |z| < 1 and Res > 1. Our earlier established results on the integral representations for the Riemann zeta function ζ(2n+1) and the Dirichlet beta function β(2n), n ∈ N, are a direct consequence of these representations. © 2006 Elsevier Inc. All rights reserved