Fungrim home page

Fungrim entry: 2a47d7

Γ(x)>(2π)1/2xx−1/2e−x\Gamma(x) > {\left(2 \pi\right)}^{1 / 2} {x}^{x - 1 / 2} {e}^{-x}
Assumptions:x∈(0,∞)x \in \left(0, \infty\right)
TeX:
\Gamma(x) > {\left(2 \pi\right)}^{1 / 2} {x}^{x - 1 / 2} {e}^{-x}

x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
GammaΓ(z)\Gamma(z) Gamma function
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
Expez{e}^{z} Exponential function
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("2a47d7"),
    Formula(Greater(Gamma(x), Mul(Mul(Pow(Mul(2, Pi), Div(1, 2)), Pow(x, Sub(x, Div(1, 2)))), Exp(Neg(x))))),
    Variables(x),
    Assumptions(Element(x, 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.

2021-03-15 19:12:00.328586 UTC