Fungrim entry: 4bf3da

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

TeX:

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

Definitions:

Fungrim symbol	Notation	Short description
`CC`	$\mathbb{C}$	Complex numbers
`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

Source code for this entry:

Entry(ID("4bf3da"),
    Formula(Implies(Element(a, SetMinus(CC, ZZLessEqual(0))), IsHolomorphic(HurwitzZeta(s, a), ForElement(s, SetMinus(CC, Set(1)))))),
    Variables(a))

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