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Fungrim entry: 345c26

ζ ⁣(2,1)=∑n=1∞Hn(n+1)2=ζ ⁣(3)\zeta\!\left(2, 1\right) = \sum_{n=1}^{\infty} \frac{H_{n}}{{\left(n + 1\right)}^{2}} = \zeta\!\left(3\right)
TeX:
\zeta\!\left(2, 1\right) = \sum_{n=1}^{\infty} \frac{H_{n}}{{\left(n + 1\right)}^{2}} = \zeta\!\left(3\right)
Definitions:
Fungrim symbol Notation Short description
MultiZetaValueζ ⁣(s1,…,sk)\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right) Multiple zeta value (MZV)
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Source code for this entry:
Entry(ID("345c26"),
    Formula(Equal(MultiZetaValue(2, 1), Sum(Div(HarmonicNumber(n), Pow(Add(n, 1), 2)), For(n, 1, Infinity)), RiemannZeta(3))))

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2021-03-15 19:12:00.328586 UTC