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Fungrim entry: a2675b

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

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 1
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
Powab{a}^{b} Power
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
    Formula(Equal(DigammaFunction(z), Add(Sub(Neg(Div(1, z)), ConstGamma), Sum(Mul(Mul(Pow(-1, Add(n, 1)), RiemannZeta(Add(n, 1))), Pow(z, n)), For(n, 1, Infinity))))),
    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