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

Halphen's constant