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Fungrim entry: c86ca1

x(xn,n+1)        ψ ⁣(x)(0,)x \in \left(x_{n}, -n + 1\right) \;\implies\; \psi\!\left(x\right) \in \left(0, \infty\right)
Assumptions:nZ1  and  xRn \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
x \in \left(x_{n}, -n + 1\right) \;\implies\; \psi\!\left(x\right) \in \left(0, \infty\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(DigammaFunctionZero(n), Add(Neg(n), 1))), Element(DigammaFunction(x), OpenInterval(0, Infinity)))),
    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