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Fungrim entry: ef8b17

ζ ⁣(s,s)=12((ζ ⁣(s))2−ζ ⁣(2s))\zeta\!\left(s, s\right) = \frac{1}{2} \left({\left(\zeta\!\left(s\right)\right)}^{2} - \zeta\!\left(2 s\right)\right)
Assumptions:s∈Z≥2s \in \mathbb{Z}_{\ge 2}
TeX:
\zeta\!\left(s, s\right) = \frac{1}{2} \left({\left(\zeta\!\left(s\right)\right)}^{2} - \zeta\!\left(2 s\right)\right)

s \in \mathbb{Z}_{\ge 2}
Definitions:
Fungrim symbol Notation Short description
MultiZetaValueζ ⁣(s1,…,sk)\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right) Multiple zeta value (MZV)
Powab{a}^{b} Power
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("ef8b17"),
    Formula(Equal(MultiZetaValue(s, s), Mul(Div(1, 2), Sub(Pow(RiemannZeta(s), 2), RiemannZeta(Mul(2, s)))))),
    Variables(s),
    Assumptions(Element(s, ZZGreaterEqual(2))))

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2021-03-15 19:12:00.328586 UTC