Fungrim entry: f045b3

s \in \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)

TeX:

s \in \{0, -1, \ldots\} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C}\right)

Definitions:

Fungrim symbol	Notation	Short description
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n
`IsHolomorphic`	$f(z) \text{ is holomorphic at } z = c$	Holomorphic predicate
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f045b3"),
    Formula(Implies(Element(s, ZZLessEqual(0)), IsHolomorphic(HurwitzZeta(s, a), ForElement(a, CC)))),
    Variables(s))

Topics using this entry

2021-03-15 19:12:00.328586 UTC