Fungrim home page

Fungrim entry: cc523f

(s{0,1,}  and  aQ)        ζ ⁣(s,a)Q\left(s \in \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{Q}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{Q}
\left(s \in \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; a \in \mathbb{Q}\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{Q}
Fungrim symbol Notation Short description
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
QQQ\mathbb{Q} Rational numbers
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Source code for this entry:
    Formula(Implies(And(Element(s, ZZLessEqual(0)), Element(a, QQ)), Element(HurwitzZeta(s, a), QQ))),
    Variables(s, a))

Topics using this entry

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