Fungrim entry: adf5e2

\psi\!\left(1 - z\right) = \psi\!\left(z\right) + \pi \cot\!\left(\pi z\right)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \mathbb{Z}

TeX:

\psi\!\left(1 - z\right) = \psi\!\left(z\right) + \pi \cot\!\left(\pi z\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("adf5e2"),
    Formula(Equal(DigammaFunction(Sub(1, z)), Add(DigammaFunction(z), Mul(Pi, Cot(Mul(Pi, z)))))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZ))))

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