Fungrim entry: cc523f

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

TeX:

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

Definitions:

Fungrim symbol	Notation	Short description
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n
`QQ`	$\mathbb{Q}$	Rational numbers
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function

Source code for this entry:

Entry(ID("cc523f"),
    Formula(Implies(And(Element(s, ZZLessEqual(0)), Element(a, QQ)), Element(HurwitzZeta(s, a), QQ))),
    Variables(s, a))

Topics using this entry

2021-03-15 19:12:00.328586 UTC