International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 417-422
doi:10.1155/S0161171294000591
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
Abstract
We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1. The idea of a q-analogue for the Euler totient function is suggested.