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Fungrim entry: a8ab81

(m∈Z≥0  and⁡  z∈C∖{0,−1,…})    ⟹    ψ(m) ⁣(z)∈C\left(m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(z\right) \in \mathbb{C}
TeX:
\left(m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(z\right) \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex 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("a8ab81"),
    Formula(Implies(And(Element(m, ZZGreaterEqual(0)), Element(z, SetMinus(CC, ZZLessEqual(0)))), Element(DigammaFunction(z, m), CC))),
    Variables(z, m))

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