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Fungrim entry: 686524

ψ ⁣(z)=γ+n=0(1n+11n+z)\psi\!\left(z\right) = -\gamma + \sum_{n=0}^{\infty} \left(\frac{1}{n + 1} - \frac{1}{n + 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) = -\gamma + \sum_{n=0}^{\infty} \left(\frac{1}{n + 1} - \frac{1}{n + 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
ConstGammaγ\gamma The constant gamma (0.577...)
Sumnf(n)\sum_{n} f(n) Sum
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("686524"),
    Formula(Equal(DigammaFunction(z), Add(Neg(ConstGamma), Sum(Parentheses(Sub(Div(1, Add(n, 1)), Div(1, Add(n, z)))), For(n, 0, Infinity))))),
    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.

2020-08-27 09:56:25.682319 UTC