Fungrim entry: 8bbb6f

\zeta\!\left(s, \frac{1}{4}\right) + \zeta\!\left(s, \frac{3}{4}\right) = {2}^{s} \left({2}^{s} - 1\right) \zeta\!\left(s\right)

Assumptions:

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1

TeX:

\zeta\!\left(s, \frac{1}{4}\right) + \zeta\!\left(s, \frac{3}{4}\right) = {2}^{s} \left({2}^{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("8bbb6f"),
    Formula(Equal(Add(HurwitzZeta(s, Div(1, 4)), HurwitzZeta(s, Div(3, 4))), Mul(Mul(Pow(2, s), Sub(Pow(2, s), 1)), RiemannZeta(s)))),
    Variables(s),
    Assumptions(And(Element(s, CC), NotEqual(s, 1))))

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