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Fungrim entry: d4bdf8

x(n,xn)        ψ ⁣(x)(,0)x \in \left(-n, x_{n}\right) \;\implies\; \psi\!\left(x\right) \in \left(-\infty, 0\right)
Assumptions:nZ1  and  xRn \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
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}
Fungrim symbol Notation Short description
OpenInterval(a,b)\left(a, b\right) Open interval
DigammaFunctionZeroxnx_{n} Zero of the digamma function
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
Infinity\infty Positive infinity
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
RRR\mathbb{R} Real numbers
Source code for this entry:
    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

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