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Fungrim entry: a9a405

n=1φ(n)nlog ⁣(1xn)=xx1\sum_{n=1}^{\infty} \frac{\varphi(n)}{n} \log\!\left(1 - {x}^{n}\right) = \frac{x}{x - 1}
Assumptions:xC  and  x<1x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|x\right| < 1
\sum_{n=1}^{\infty} \frac{\varphi(n)}{n} \log\!\left(1 - {x}^{n}\right) = \frac{x}{x - 1}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|x\right| < 1
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
Totientφ(n)\varphi(n) Euler totient function
Loglog(z)\log(z) Natural logarithm
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
    Formula(Equal(Sum(Mul(Div(Totient(n), n), Log(Sub(1, Pow(x, n)))), For(n, 1, Infinity)), Div(x, Sub(x, 1)))),
    Assumptions(And(Element(x, CC), Less(Abs(x), 1))))

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2021-03-15 19:12:00.328586 UTC