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Fungrim entry: 233814

xn=zero*xSψ ⁣(x)   where S={(0,),n=0(n,n+1),n<0x_{n} = \mathop{\operatorname{zero*}\,}\limits_{x \in S} \psi\!\left(x\right)\; \text{ where } S = \begin{cases} \left(0, \infty\right), & n = 0\\\left(-n, -n + 1\right), & n < 0\\ \end{cases}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
x_{n} = \mathop{\operatorname{zero*}\,}\limits_{x \in S} \psi\!\left(x\right)\; \text{ where } S = \begin{cases} \left(0, \infty\right), & n = 0\\\left(-n, -n + 1\right), & n < 0\\ \end{cases}

n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
DigammaFunctionZeroxnx_{n} Zero of the digamma function
UniqueZerozero*xSf(x)\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x) Unique zero (root) of function
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(DigammaFunctionZero(n), Where(UniqueZero(DigammaFunction(x), ForElement(x, S)), Equal(S, Cases(Tuple(OpenInterval(0, Infinity), Equal(n, 0)), Tuple(OpenInterval(Neg(n), Add(Neg(n), 1)), Less(n, 0))))))),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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2021-03-15 19:12:00.328586 UTC