Fungrim entry: d4bdf8

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

Assumptions:

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}

TeX:

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

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; 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
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("d4bdf8"),
    Formula(Implies(Element(x, OpenInterval(Neg(n), DigammaFunctionZero(n))), Element(DigammaFunction(x), OpenInterval(Neg(Infinity), 0)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(x, RR))))

Topics using this entry

Digamma function