Fungrim entry: 8671a4

{\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) < \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{{x}^{m + 1}}

Assumptions:

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)

TeX:

{\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) < \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{{x}^{m + 1}}

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`Factorial`	$n !$	Factorial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("8671a4"),
    Formula(Less(Mul(Pow(-1, Add(m, 1)), DigammaFunction(x, m)), Add(Div(Factorial(Sub(m, 1)), Pow(x, m)), Div(Factorial(m), Pow(x, Add(m, 1)))))),
    Variables(m, x),
    Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(x, OpenInterval(0, Infinity)))))

Topics using this entry

Digamma function