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Fungrim entry: e1e71f

ψ ⁣(z)=0(et1(1+t)z)1tdt\psi\!\left(z\right) = \int_{0}^{\infty} \left({e}^{-t} - \frac{1}{{\left(1 + t\right)}^{z}}\right) \frac{1}{t} \, dt
Assumptions:zC  and  Re(z)>0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0
\psi\!\left(z\right) = \int_{0}^{\infty} \left({e}^{-t} - \frac{1}{{\left(1 + t\right)}^{z}}\right) \frac{1}{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
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Expez{e}^{z} Exponential function
Powab{a}^{b} Power
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), Integral(Mul(Parentheses(Sub(Exp(Neg(t)), Div(1, Pow(Add(1, t), z)))), Div(1, 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