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Fungrim entry: 4e3853

n=1ψ ⁣(n)zn=z(γ+log ⁣(1z))z1\sum_{n=1}^{\infty} \psi\!\left(n\right) {z}^{n} = \frac{z \left(\gamma + \log\!\left(1 - z\right)\right)}{z - 1}
Assumptions:zC  and  z<1z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 1
\sum_{n=1}^{\infty} \psi\!\left(n\right) {z}^{n} = \frac{z \left(\gamma + \log\!\left(1 - z\right)\right)}{z - 1}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 1
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Powab{a}^{b} Power
Infinity\infty Positive infinity
ConstGammaγ\gamma The constant gamma (0.577...)
Loglog(z)\log(z) Natural logarithm
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
    Formula(Equal(Sum(Mul(DigammaFunction(n), Pow(z, n)), For(n, 1, Infinity)), Div(Mul(z, Add(ConstGamma, Log(Sub(1, z)))), Sub(z, 1)))),
    Assumptions(And(Element(z, CC), Less(Abs(z), 1))))

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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