TL;DR
This paper presents a novel infinite product representation for the mathematical constant e, involving the golden ratio, Möbius function, and Euler phi function, linking number theory concepts to e.
Contribution
It introduces a new infinite product formula for e that incorporates key number theory functions and the golden ratio, expanding understanding of e's properties.
Findings
Derived an infinite product involving e, the golden ratio, Möbius, and Euler phi functions.
Established connections between e and fundamental number theory functions.
Provides a new perspective on the mathematical structure of e.
Abstract
We prove an infinite product representation for the constant involving the golden ratio, the M\"obius function and the Euler phi function - prominent players in number theory.
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