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

Hurwitz zeta function