A new class of infinite products, and Euler's totient
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...
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Main Author: | Geoffrey B. Campbell |
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Format: | Article |
Language: | English |
Published: |
Wiley
1994-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
Subjects: | |
Online Access: | http://dx.doi.org/10.1155/S0161171294000591 |
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