Fungrim home page

Fungrim entry: 0e5d90

(mZ1  and  m odd  and  xR{0,1,})        ψ(m) ⁣(x)(0,)\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)
Assumptions:mZ1  and  xRm \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
\left(m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; m \text{ odd} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R} \setminus \{0, -1, \ldots\}\right) \;\implies\; \psi^{(m)}\!\left(x\right) \in \left(0, \infty\right)

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
Fungrim symbol Notation Short description
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
RRR\mathbb{R} Real numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Implies(And(Element(m, ZZGreaterEqual(1)), Odd(m), Element(x, SetMinus(RR, ZZLessEqual(0)))), Element(DigammaFunction(x, m), OpenInterval(0, Infinity)))),
    Variables(x, m),
    Assumptions(And(Element(m, 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