Fungrim entry: da71d3

\zeta\!\left(a, b\right) + \zeta\!\left(b, a\right) = \zeta\!\left(a\right) \zeta\!\left(b\right) - \zeta\!\left(a + b\right)

Assumptions:

a \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; b \in \mathbb{Z}_{\ge 2}

TeX:

\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}

Definitions:

Fungrim symbol	Notation	Short description
`MultiZetaValue`	$\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right)$	Multiple zeta value (MZV)
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("da71d3"),
    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)))))

Topics using this entry

Multiple zeta values