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Fungrim entry: 394cdc

ψ(m) ⁣(z) is holomorphic on z∈C∖{0,−1,…}\psi^{(m)}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \{0, -1, \ldots\}
Assumptions:m∈Z≥0m \in \mathbb{Z}_{\ge 0}
TeX:
\psi^{(m)}\!\left(z\right) \text{ is holomorphic on } z \in \mathbb{C} \setminus \{0, -1, \ldots\}

m \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
CCC\mathbb{C} Complex numbers
ZZLessEqualZ≤n\mathbb{Z}_{\le n} Integers less than or equal to n
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("394cdc"),
    Formula(IsHolomorphic(DigammaFunction(z, m), ForElement(z, SetMinus(CC, ZZLessEqual(0))))),
    Variables(m),
    Assumptions(Element(m, ZZGreaterEqual(0))))

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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