Fungrim entry: 3c4f5f

x \in \left(0, x_{0}\right) \;\implies\; \psi\!\left(x\right) \in \left(-\infty, 0\right)

Assumptions:

x \in \mathbb{R}

TeX:

x \in \left(0, x_{0}\right) \;\implies\; \psi\!\left(x\right) \in \left(-\infty, 0\right)

x \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`OpenInterval`	$\left(a, b\right)$	Open interval
`DigammaFunctionZero`	$x_{n}$	Zero of the digamma function
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`Infinity`	$\infty$	Positive infinity
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("3c4f5f"),
    Formula(Implies(Element(x, OpenInterval(0, DigammaFunctionZero(0))), Element(DigammaFunction(x), OpenInterval(Neg(Infinity), 0)))),
    Variables(x),
    Assumptions(Element(x, RR)))

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