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Fungrim entry: d0bba3

(m∈Z≥0  and⁡  x∈R∖{0,−1,…})    ⟹    ψ(m) ⁣(x)∈R\left(m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \mathbb{R}
TeX:
\left(m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
RRR\mathbb{R} Real numbers
ZZLessEqualZ≤n\mathbb{Z}_{\le n} Integers less than or equal to n
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Source code for this entry:
Entry(ID("d0bba3"),
    Formula(Implies(And(Element(m, ZZGreaterEqual(0)), Element(x, SetMinus(RR, ZZLessEqual(0)))), Element(DigammaFunction(x, m), RR))),
    Variables(x, m))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC