# Fungrim entry: 4d1f6b

$\zeta\!\left(s, \frac{1}{6}\right) + \zeta\!\left(s, \frac{5}{6}\right) = \left({2}^{s} - 1\right) \left({3}^{s} - 1\right) \zeta\!\left(s\right)$
Assumptions:$s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1$
TeX:
\zeta\!\left(s, \frac{1}{6}\right) + \zeta\!\left(s, \frac{5}{6}\right) = \left({2}^{s} - 1\right) \left({3}^{s} - 1\right) \zeta\!\left(s\right)

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1
Definitions:
Fungrim symbol Notation Short description
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
Pow${a}^{b}$ Power
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("4d1f6b"),
Formula(Equal(Add(HurwitzZeta(s, Div(1, 6)), HurwitzZeta(s, Div(5, 6))), Mul(Mul(Sub(Pow(2, s), 1), Sub(Pow(3, s), 1)), RiemannZeta(s)))),
Variables(s),
Assumptions(And(Element(s, CC), NotEqual(s, 1))))

## 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