Fungrim entry: 31adf6

\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

Halphen's constant