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Fungrim entry: b16177

{ψ(m) ⁣(x+y)>ψ ⁣(x),m evenψ(m) ⁣(x+y)<ψ ⁣(x),m odd\begin{cases} \psi^{(m)}\!\left(x + y\right) > \psi\!\left(x\right), & m \text{ even}\\\psi^{(m)}\!\left(x + y\right) < \psi\!\left(x\right), & m \text{ odd}\\ \end{cases}
Assumptions:mZ0  and  x(0,)  and  y(0,)m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
\begin{cases} \psi^{(m)}\!\left(x + y\right) > \psi\!\left(x\right), & m \text{ even}\\\psi^{(m)}\!\left(x + y\right) < \psi\!\left(x\right), & m \text{ odd}\\ \end{cases}

m \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right)
Fungrim symbol Notation Short description
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
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(Cases(Tuple(Greater(DigammaFunction(Add(x, y), m), DigammaFunction(x)), Even(m)), Tuple(Less(DigammaFunction(Add(x, y), m), DigammaFunction(x)), Odd(m)))),
    Variables(x, y, m),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)))))

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2021-03-15 19:12:00.328586 UTC