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Fungrim entry: a0ca3e

Γ(x)<(2π)1/2xx1/2exexp ⁣(112x)\Gamma(x) < {\left(2 \pi\right)}^{1 / 2} {x}^{x - 1 / 2} {e}^{-x} \exp\!\left(\frac{1}{12 x}\right)
Assumptions:x(0,)x \in \left(0, \infty\right)
TeX:
\Gamma(x) < {\left(2 \pi\right)}^{1 / 2} {x}^{x - 1 / 2} {e}^{-x} \exp\!\left(\frac{1}{12 x}\right)

x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
GammaFunctionΓ(z)\Gamma(z) Gamma function
Powab{a}^{b} Power
ConstPiπ\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("a0ca3e"),
    Formula(Less(GammaFunction(x), Mul(Mul(Mul(Pow(Mul(2, ConstPi), Div(1, 2)), Pow(x, Sub(x, Div(1, 2)))), Exp(Neg(x))), Exp(Div(1, Mul(12, x)))))),
    Variables(x),
    Assumptions(Element(x, OpenInterval(0, Infinity))))

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

2019-10-05 13:11:19.856591 UTC