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Fungrim entry: e7224b

(sR{1}  and  a(0,))        ζ ⁣(s,a)R\left(s \in \mathbb{R} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \left(0, \infty\right)\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{R}
\left(s \in \mathbb{R} \setminus \left\{1\right\} \;\mathbin{\operatorname{and}}\; a \in \left(0, \infty\right)\right) \;\implies\; \zeta\!\left(s, a\right) \in \mathbb{R}
Fungrim symbol Notation Short description
RRR\mathbb{R} Real numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Source code for this entry:
    Formula(Implies(And(Element(s, SetMinus(RR, Set(1))), Element(a, OpenInterval(0, Infinity))), Element(HurwitzZeta(s, a), RR))),
    Variables(s, a))

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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