# Fungrim entry: a4cc3b

$\psi\!\left(z\right) = -\gamma + \int_{0}^{1} \frac{1 - {t}^{z - 1}}{1 - t} \, dt$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0$
TeX:
\psi\!\left(z\right) = -\gamma + \int_{0}^{1} \frac{1 - {t}^{z - 1}}{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
ConstGamma$\gamma$ The constant gamma (0.577...)
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("a4cc3b"),
Formula(Equal(DigammaFunction(z), Add(Neg(ConstGamma), Integral(Div(Sub(1, Pow(t, Sub(z, 1))), Sub(1, t)), For(t, 0, 1))))),
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