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Fungrim entry: ebc49c

ζ ⁣(s,a)=12s(ζ ⁣(s,a2)+ζ ⁣(s,a+12))\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:sC  and  aC  and  s1  and  Re(a)>0s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; s \ne 1 \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
\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
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    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))))

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2021-03-15 19:12:00.328586 UTC