International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 417-422

A new class of infinite products, and Euler's totient

Geoffrey B. Campbell

Mathematics Research Section, Institute of Advanced Studies, School of Mathematical Sciences, The Australian National University, GPO Box 4, Canberra 2601, Australia

Received 31 May 1991; Revised 2 September 1993

Copyright © 1994 Geoffrey B. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce some new infinite products, the simplest being(1y)k=2jϕk(1ykqj)1/k=(1y1qy)1/(1q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y||qy| both less than unity, with q1. The idea of a q-analogue for the Euler totient function is suggested.