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Fungrim entry: 4a23c7

ζ ⁣(2,,2n times)=π2n(2n+1)!\zeta\!\left(\underbrace{2, \ldots, 2}_{n \text{ times}}\right) = \frac{{\pi}^{2 n}}{\left(2 n + 1\right)!}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
\zeta\!\left(\underbrace{2, \ldots, 2}_{n \text{ times}}\right) = \frac{{\pi}^{2 n}}{\left(2 n + 1\right)!}

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
MultiZetaValueζ ⁣(s1,,sk)\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right) Multiple zeta value (MZV)
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
Factorialn!n ! Factorial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(MultiZetaValue(Repeat(2, n)), Div(Pow(Pi, Mul(2, n)), Factorial(Add(Mul(2, n), 1))))),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC