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Fungrim entry: f946a5

ψ ⁣(z)=γ+0etezt1etdt\psi\!\left(z\right) = -\gamma + \int_{0}^{\infty} \frac{{e}^{-t} - {e}^{-z t}}{1 - {e}^{-t}} \, dt
Assumptions:zC  and  Re(z)>0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
\psi\!\left(z\right) = -\gamma + \int_{0}^{\infty} \frac{{e}^{-t} - {e}^{-z t}}{1 - {e}^{-t}} \, dt

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
ConstGammaγ\gamma The constant gamma (0.577...)
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Expez{e}^{z} Exponential function
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    Formula(Equal(DigammaFunction(z), Add(Neg(ConstGamma), Integral(Div(Sub(Exp(Neg(t)), Exp(Neg(Mul(z, t)))), Sub(1, Exp(Neg(t)))), For(t, 0, Infinity))))),
    Assumptions(And(Element(z, CC), Greater(Re(z), 0))))

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2021-03-15 19:12:00.328586 UTC