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Fungrim entry: 5a3c4a

(1)m+1ψ(m) ⁣(x)>(m1)!xm+m!2xm+1{\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) > \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{2 {x}^{m + 1}}
Assumptions:mZ1  and  x(0,)m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
{\left(-1\right)}^{m + 1} \psi^{(m)}\!\left(x\right) > \frac{\left(m - 1\right)!}{{x}^{m}} + \frac{m !}{2 {x}^{m + 1}}

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right)
Fungrim symbol Notation Short description
Powab{a}^{b} Power
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Factorialn!n ! Factorial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Greater(Mul(Pow(-1, Add(m, 1)), DigammaFunction(x, m)), Add(Div(Factorial(Sub(m, 1)), Pow(x, m)), Div(Factorial(m), Mul(2, Pow(x, Add(m, 1))))))),
    Variables(m, x),
    Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(x, OpenInterval(0, Infinity)))))

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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