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Fungrim entry: 831ea4

Λ=zero*x(0,1)[18+n=1dn(1)ddxn]\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[-\frac{1}{8} + \sum_{n=1}^{\infty} \left|\sum_{d \mid n} {\left(-1\right)}^{d} d\right| {x}^{n}\right]
TeX:
\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[-\frac{1}{8} + \sum_{n=1}^{\infty} \left|\sum_{d \mid n} {\left(-1\right)}^{d} d\right| {x}^{n}\right]
Definitions:
Fungrim symbol Notation Short description
HalphenConstantΛ\Lambda Halphen's constant (one-ninth constant) 0.10765...
UniqueZerozero*xSf(x)\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x) Unique zero (root) of function
Sumnf(n)\sum_{n} f(n) Sum
Absz\left|z\right| Absolute value
DivisorSumknf(k)\sum_{k \mid n} f(k) Sum over divisors
Powab{a}^{b} Power
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("831ea4"),
    Formula(Equal(HalphenConstant, UniqueZero(Add(Neg(Div(1, 8)), Sum(Mul(Abs(DivisorSum(Mul(Pow(-1, d), d), For(d, n))), Pow(x, n)), For(n, 1, Infinity))), ForElement(x, OpenInterval(0, 1))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC