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Fungrim entry: ee3dc5

ψ ⁣(z)=(z1)3F2 ⁣(1,1,2z,2,2,1)γ\psi\!\left(z\right) = \left(z - 1\right) \,{}_3F_2\!\left(1, 1, 2 - z, 2, 2, 1\right) - \gamma
Assumptions:zC  and  Re(z)>0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
References:
  • http://functions.wolfram.com/GammaBetaErf/PolyGamma/26/01/01/0001/
TeX:
\psi\!\left(z\right) = \left(z - 1\right) \,{}_3F_2\!\left(1, 1, 2 - z, 2, 2, 1\right) - \gamma

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
Definitions:
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
ConstGammaγ\gamma The constant gamma (0.577...)
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
Entry(ID("ee3dc5"),
    Formula(Equal(DigammaFunction(z), Sub(Mul(Sub(z, 1), Hypergeometric3F2(1, 1, Sub(2, z), 2, 2, 1)), ConstGamma))),
    Variables(z),
    Assumptions(And(Element(z, CC), Greater(Re(z), 0))),
    References("http://functions.wolfram.com/GammaBetaErf/PolyGamma/26/01/01/0001/"))

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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