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Fungrim entry: 8bbb6f

ζ ⁣(s,14)+ζ ⁣(s,34)=2s(2s1)ζ ⁣(s)\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:sC  and  s1s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1
\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
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Powab{a}^{b} Power
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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)))),
    Assumptions(And(Element(s, CC), NotEqual(s, 1))))

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2021-03-15 19:12:00.328586 UTC