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

Geoffrey B. Campbell

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-6

Abstract:

We introduce some new infinite products, the simplest being ( 1 − y ) ∏ k = 2 ∞ ∏ j ∈ ϕ k ( 1 − y k q j ) 1 / k = ( 1 − y 1 − q y ) 1 / ( 1 − q ) , where ϕ k is the set of positive integers less than and relatively prime to k , valid for | y | ∧ | q y | both less than unity, with q ≠ 1 . The idea of a q -analogue for the Euler totient function is suggested.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:924852

DOI: 10.1155/S0161171294000591

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