Fungrim entry: 6419ac

\zeta\!\left(2, a\right) = {a}^{-2} \,{}_3F_2\!\left(1, a, a, a + 1, a + 1, 1\right)

Assumptions:

a \in \mathbb{C} \setminus \{0, -1, \ldots\}

TeX:

\zeta\!\left(2, a\right) = {a}^{-2} \,{}_3F_2\!\left(1, a, a, a + 1, a + 1, 1\right)

a \in \mathbb{C} \setminus \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("6419ac"),
    Formula(Equal(HurwitzZeta(2, a), Mul(Pow(a, -2), Hypergeometric3F2(1, a, a, Add(a, 1), Add(a, 1), 1)))),
    Variables(a),
    Assumptions(Element(a, SetMinus(CC, ZZLessEqual(0)))))

Topics using this entry

Hurwitz zeta function

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