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Fungrim entry: 70c42b

ζ ⁣(3,1,…,3,1⏟(3,1)  n times)=12n+1ζ ⁣(2,…,2⏟2n times)\zeta\!\left(\underbrace{3, 1, \ldots, 3, 1}_{\left(3, 1\right) \; n \text{ times}}\right) = \frac{1}{2 n + 1} \zeta\!\left(\underbrace{2, \ldots, 2}_{2 n \text{ times}}\right)
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\zeta\!\left(\underbrace{3, 1, \ldots, 3, 1}_{\left(3, 1\right) \; n \text{ times}}\right) = \frac{1}{2 n + 1} \zeta\!\left(\underbrace{2, \ldots, 2}_{2 n \text{ times}}\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
MultiZetaValueζ ⁣(s1,…,sk)\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right) Multiple zeta value (MZV)
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("70c42b"),
    Formula(Equal(MultiZetaValue(Repeat(3, 1, n)), Mul(Div(1, Add(Mul(2, n), 1)), MultiZetaValue(Repeat(2, Mul(2, n)))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(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