# Fungrim entry: e1e71f

$\psi\!\left(z\right) = \int_{0}^{\infty} \left({e}^{-t} - \frac{1}{{\left(1 + t\right)}^{z}}\right) \frac{1}{t} \, dt$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0$
TeX:
\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
Definitions:
Fungrim symbol Notation Short description
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Exp${e}^{z}$ Exponential function
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("e1e71f"),
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)))),
Variables(z),
Assumptions(And(Element(z, CC), Greater(Re(z), 0))))

## Topics using this entry

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