Integral representations of the Legendre chi function

Abstract

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