Fungrim entry: 4a23c7

\zeta\!\left(\underbrace{2, \ldots, 2}_{n \text{ times}}\right) = \frac{{\pi}^{2 n}}{\left(2 n + 1\right)!}

Assumptions:

n \in \mathbb{Z}_{\ge 1}

TeX:

\zeta\!\left(\underbrace{2, \ldots, 2}_{n \text{ times}}\right) = \frac{{\pi}^{2 n}}{\left(2 n + 1\right)!}

n \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`MultiZetaValue`	$\zeta\!\left({s}_{1}, \ldots, {s}_{k}\right)$	Multiple zeta value (MZV)
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Factorial`	$n !$	Factorial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("4a23c7"),
    Formula(Equal(MultiZetaValue(Repeat(2, n)), Div(Pow(Pi, Mul(2, n)), Factorial(Add(Mul(2, n), 1))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

Multiple zeta values

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