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We introduce some new infinite products, the simplest being(1Ã¢ÂˆÂ’y)Ã¢ÂˆÂk=2Ã¢ÂˆÂžÃ¢ÂˆÂjÃ¢ÂˆÂˆÃÂ•k(1Ã¢ÂˆÂ’ykqj)1/k=(1Ã¢ÂˆÂ’y1Ã¢ÂˆÂ’qy)1/(1Ã¢ÂˆÂ’q),where ÃÂ•k is the set of positive integers less than and relatively prime to k, valid for |y|Ã¢ÂˆÂ§|qy| both less than unity, with qÃ¢Â‰Â 1. The idea of a q-analogue for the Euler totient function is suggested

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