Fungrim entry: 05c2dd

s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } a \in \mathbb{C}\right)

TeX:

s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is meromorphic on } a \in \mathbb{C}\right)

Definitions:

Fungrim symbol	Notation	Short description
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`IsMeromorphic`	$f(z) \text{ is meromorphic at } z = c$	Meromorphic predicate
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("05c2dd"),
    Formula(Implies(Element(s, ZZGreaterEqual(2)), IsMeromorphic(HurwitzZeta(s, a), ForElement(a, CC)))),
    Variables(s))

Topics using this entry

2021-03-15 19:12:00.328586 UTC