$\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[\sum_{n=0}^{\infty} {\left(2 n + 1\right)}^{2} {\left(-x\right)}^{n \left(n + 1\right) / 2}\right]$
TeX:
\Lambda = \mathop{\operatorname{zero*}\,}\limits_{x \in \left(0, 1\right)} \left[\sum_{n=0}^{\infty} {\left(2 n + 1\right)}^{2} {\left(-x\right)}^{n \left(n + 1\right) / 2}\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("31adf6"),
Formula(Equal(HalphenConstant, UniqueZero(Brackets(Sum(Mul(Pow(Add(Mul(2, n), 1), 2), Pow(Neg(x), Div(Mul(n, Add(n, 1)), 2))), For(n, 0, 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.

2021-03-15 19:12:00.328586 UTC