Integral representations of the Legendre chi function

Abstract

We, by making use of elementary arguments, deduce integral representations of the Legendre chi function chi(S)(z) valid for vertical bar z vertical bar LT 1 and Res GT 1. Our earlier established results on the integral representations for the Riemann zeta function zeta(2n + 1) and the Dirichlet beta function beta(2n), n epsilon N, are a direct consequence of these representations. (c) 2006 Elsevier Inc. All rights reserved.