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Fungrim entry: 4b6ccb

ψ ⁣(z)=ddz[logΓ(z)]\psi\!\left(z\right) = \frac{d}{d z}\, \left[\log \Gamma(z)\right]
Assumptions:zC  and  z{0,1,}z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
TeX:
\psi\!\left(z\right) = \frac{d}{d z}\, \left[\log \Gamma(z)\right]

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
ComplexBranchDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative, allowing branch cuts
LogGammalogΓ(z)\log \Gamma(z) Logarithmic gamma function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("4b6ccb"),
    Formula(Equal(DigammaFunction(z), ComplexBranchDerivative(Brackets(LogGamma(z)), For(z, z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(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