A further note on Ramanujan's arithmetical function τ(n)

Abstract

This note is a sequel to two in earlier volumes of the Proceedings, the first by myself and the second by Wilton†.Suppose thatfor |z| <1; that x > 0; thatforr ≥ 0; and thatwhere τ(x) is to mean 0 if x is not an integer. Thuswhere the dash shows that the last term is to be halved when x is an integer;forr > 1; and