On the numerical evaluation of Legendre's chi-function

Legendre's chi-function, [formula] , is reexpanded in a power series in powers of [formula] . The expansion obtained is well suited for the computation of [formula] in the two cases of real z close to 1, and [formula] . For n=2 and n=3 , the present computational procedure is shown to be superior to the procedure recently proposed by Dempsey, Liu, and Dempsey, which uses Plana's summation formula.