Fungrim entry: 0e5d90

\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)

Assumptions:

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

TeX:

\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`RR`	$\mathbb{R}$	Real numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0e5d90"),
    Formula(Implies(And(Element(m, ZZGreaterEqual(1)), Odd(m), Element(x, SetMinus(RR, ZZLessEqual(0)))), Element(DigammaFunction(x, m), OpenInterval(0, Infinity)))),
    Variables(x, m),
    Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(x, RR))))

Topics using this entry

Digamma function