# Fungrim entry: 9758ac

$\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[-\frac{1}{8} + \sum_{n=1}^{\infty} \frac{n {x}^{n}}{1 - {\left(-x\right)}^{n}}\right]$
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
HalphenConstant$\Lambda$ Halphen's constant (one-ninth constant) 0.10765...
UniqueZero$\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x)$ Unique zero (root) of function
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
OpenInterval$\left(a, b\right)$ 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))))))

## Topics using this entry

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