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Fungrim entry: 693e0e

ψ ⁣(z)=lims1[1s1ζ ⁣(s,z)]\psi\!\left(z\right) = \lim_{s \to 1} \left[\frac{1}{s - 1} - \zeta\!\left(s, z\right)\right]
Assumptions:zC{0,1,}z \in \mathbb{C} \setminus \{0, -1, \ldots\}
\psi\!\left(z\right) = \lim_{s \to 1} \left[\frac{1}{s - 1} - \zeta\!\left(s, z\right)\right]

z \in \mathbb{C} \setminus \{0, -1, \ldots\}
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
ComplexLimitlimzaf(z)\lim_{z \to a} f(z) Limiting value, complex variable
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(DigammaFunction(z), ComplexLimit(Brackets(Sub(Div(1, Sub(s, 1)), HurwitzZeta(s, z))), For(s, 1)))),
    Assumptions(Element(z, SetMinus(CC, 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