Fungrim entry: d0b234

\left(s \in \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \zeta\!\left(s, a\right) \in \left\{{\tilde \infty}\right\}

TeX:

\left(s \in \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \zeta\!\left(s, a\right) \in \left\{{\tilde \infty}\right\}

Definitions:

Fungrim symbol	Notation	Short description
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity

Source code for this entry:

Entry(ID("d0b234"),
    Formula(Implies(And(Element(s, Set(1)), Element(a, SetMinus(CC, ZZLessEqual(0)))), Element(HurwitzZeta(s, a), Set(UnsignedInfinity)))),
    Variables(s, 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