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Fungrim entry: 5db5f2

ψ(m) ⁣(z‾)=ψ(m) ⁣(z)‾\psi^{(m)}\!\left(\overline{z}\right) = \overline{\psi^{(m)}\!\left(z\right)}
Assumptions:m∈Z≥0  and⁡  z∈Cm \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
\psi^{(m)}\!\left(\overline{z}\right) = \overline{\psi^{(m)}\!\left(z\right)}

m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Conjugatez‾\overline{z} Complex conjugate
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("5db5f2"),
    Formula(Equal(DigammaFunction(Conjugate(z), m), Conjugate(DigammaFunction(z, m)))),
    Variables(m, z),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(z, CC))))

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