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

Digamma function

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