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Fungrim entry: adf5e2

ψ ⁣(1z)=ψ ⁣(z)+πcot ⁣(πz)\psi\!\left(1 - z\right) = \psi\!\left(z\right) + \pi \cot\!\left(\pi z\right)
Assumptions:zC  and  zZz \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
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
ZZZ\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

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