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Fungrim entry: da71d3

ζ ⁣(a,b)+ζ ⁣(b,a)=ζ ⁣(a)ζ ⁣(b)ζ ⁣(a+b)\zeta\!\left(a, b\right) + \zeta\!\left(b, a\right) = \zeta\!\left(a\right) \zeta\!\left(b\right) - \zeta\!\left(a + b\right)
Assumptions:aZ2  and  bZ2a \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}_{\ge 2}
\zeta\!\left(a, b\right) + \zeta\!\left(b, a\right) = \zeta\!\left(a\right) \zeta\!\left(b\right) - \zeta\!\left(a + b\right)

a \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}_{\ge 2}
Fungrim symbol Notation Short description
MultiZetaValueζ ⁣(s1,,sk)\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right) Multiple zeta value (MZV)
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(Add(MultiZetaValue(a, b), MultiZetaValue(b, a)), Sub(Mul(RiemannZeta(a), RiemannZeta(b)), RiemannZeta(Add(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, ZZGreaterEqual(2)), Element(b, ZZGreaterEqual(2)))))

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2021-03-15 19:12:00.328586 UTC