On the remainder of a series representation for π^3

Abstract

The main motivation for obtaining the results reported in the present paper comes from the following existing identity: We obtain the asymptotic expansion of the remainder R n as given below: We also give a recursive relation for determining the coefficients involved in the obtained expansion. Moreover, we establish an upper bound and a lower bound on the remainder R n . As an application of the obtained bounds, we give an approximate value of π .