# Fungrim entry: 06c468

$\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[\theta''_{2}\!\left(0 , \frac{\log\!\left(-x\right)}{2 \pi i}\right)\right]$
TeX:
\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[\theta''_{2}\!\left(0 , \frac{\log\!\left(-x\right)}{2 \pi i}\right)\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
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Log$\log(z)$ Natural logarithm
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
OpenInterval$\left(a, b\right)$ Open interval
Source code for this entry:
Entry(ID("06c468"),
Formula(Equal(HalphenConstant, UniqueZero(Brackets(JacobiTheta(2, 0, Div(Log(Neg(x)), Mul(Mul(2, Pi), ConstI)), 2)), 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.

2021-03-15 19:12:00.328586 UTC