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Fungrim entry: 9758ac

Λ=zero*⁡ x∈(0,1)[−18+∑n=1∞nxn1−(−x)n]\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[-\frac{1}{8} + \sum_{n=1}^{\infty} \frac{n {x}^{n}}{1 - {\left(-x\right)}^{n}}\right]
TeX:
\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[-\frac{1}{8} + \sum_{n=1}^{\infty} \frac{n {x}^{n}}{1 - {\left(-x\right)}^{n}}\right]
Definitions:
Fungrim symbol Notation Short description
HalphenConstantΛ\Lambda Halphen's constant (one-ninth constant) 0.10765...
UniqueZerozero*⁡ x∈Sf(x)\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x) Unique zero (root) of function
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("9758ac"),
    Formula(Equal(HalphenConstant, UniqueZero(Add(Neg(Div(1, 8)), Sum(Div(Mul(n, Pow(x, n)), Sub(1, Pow(Neg(x), n))), For(n, 1, Infinity))), ForElement(x, OpenInterval(0, 1))))))

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2021-03-15 19:12:00.328586 UTC