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

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