Fungrim entry: 8c7cdb

s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right)

TeX:

s \in \mathbb{Z}_{\ge 2} \;\implies\; \left(\zeta\!\left(s, a\right) \text{ is holomorphic on } a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right)

Definitions:

Fungrim symbol	Notation	Short description
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater 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
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("8c7cdb"),
    Formula(Implies(Element(s, ZZGreaterEqual(2)), IsHolomorphic(HurwitzZeta(s, a), ForElement(a, SetMinus(CC, ZZLessEqual(0)))))),
    Variables(s))

Topics using this entry

Hurwitz zeta function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC