Fungrim entry: 4b6ccb

\psi\!\left(z\right) = \frac{d}{d z}\, \left[\log \Gamma(z)\right]

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

TeX:

\psi\!\left(z\right) = \frac{d}{d z}\, \left[\log \Gamma(z)\right]

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`ComplexBranchDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative, allowing branch cuts
`LogGamma`	$\log \Gamma(z)$	Logarithmic gamma function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("4b6ccb"),
    Formula(Equal(DigammaFunction(z), ComplexBranchDerivative(Brackets(LogGamma(z)), For(z, z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(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