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Fungrim entry: 4b5b44

limnφ ⁣(n)n1δ=\lim_{n \to \infty} \frac{\varphi\!\left(n\right)}{{n}^{1 - \delta}} = \infty
Assumptions:δ(0,)\delta \in \left(0, \infty\right)
TeX:
\lim_{n \to \infty} \frac{\varphi\!\left(n\right)}{{n}^{1 - \delta}} = \infty

\delta \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
SequenceLimitlimnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
Powab{a}^{b} Power
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("4b5b44"),
    Formula(Equal(SequenceLimit(Div(Totient(n), Pow(n, Sub(1, delta))), Var(n), Infinity), Infinity)),
    Variables(delta),
    Assumptions(Element(delta, OpenInterval(0, Infinity))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-20 18:07:53.062439 UTC