Fungrim entry: 233814

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}

Assumptions:

n \in \mathbb{Z}_{\ge 0}

TeX:

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}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunctionZero`	$x_{n}$	Zero of the digamma function
`UniqueZero`	$\mathop{\operatorname{zero*}\,}\limits_{x \in S} f(x)$	Unique zero (root) of function
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("233814"),
    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))))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

Topics using this entry

Digamma function