# Fungrim entry: ebc49c

$\zeta\!\left(s, a\right) = \frac{1}{{2}^{s}} \left(\zeta\!\left(s, \frac{a}{2}\right) + \zeta\!\left(s, \frac{a + 1}{2}\right)\right)$
Assumptions:$s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1 \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0$
TeX:
\zeta\!\left(s, a\right) = \frac{1}{{2}^{s}} \left(\zeta\!\left(s, \frac{a}{2}\right) + \zeta\!\left(s, \frac{a + 1}{2}\right)\right)

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1 \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
Definitions:
Fungrim symbol Notation Short description
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("ebc49c"),
Formula(Equal(HurwitzZeta(s, a), Mul(Div(1, Pow(2, s)), Add(HurwitzZeta(s, Div(a, 2)), HurwitzZeta(s, Div(Add(a, 1), 2)))))),
Variables(s, a),
Assumptions(And(Element(s, CC), Element(a, CC), NotEqual(s, 1), Greater(Re(a), 0))))

## Topics using this entry

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