# Fungrim entry: cfb999

$\psi\!\left(z\right) = \log(z) + \int_{0}^{\infty} {e}^{-z t} \left(\frac{1}{t} - \frac{1}{1 - {e}^{-t}}\right) \, dt$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0$
TeX:
\psi\!\left(z\right) = \log(z) + \int_{0}^{\infty} {e}^{-z t} \left(\frac{1}{t} - \frac{1}{1 - {e}^{-t}}\right) \, 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
Log$\log(z)$ Natural logarithm
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Exp${e}^{z}$ Exponential function
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("cfb999"),
Formula(Equal(DigammaFunction(z), Add(Log(z), Integral(Mul(Exp(Neg(Mul(z, t))), Parentheses(Sub(Div(1, t), Div(1, Sub(1, Exp(Neg(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