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Fungrim entry: 31adf6

Λ=zero*x(0,1)[n=0(2n+1)2(x)n(n+1)/2]\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]
\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]
Fungrim symbol Notation Short description
HalphenConstantΛ\Lambda Halphen's constant (one-ninth constant) 0.10765...
UniqueZerozero*xSf(x)\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x) Unique zero (root) of function
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
    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))))))

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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