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Fungrim entry: 2a47d7

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

x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) 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("2a47d7"),
    Formula(Greater(GammaFunction(x), Mul(Mul(Pow(Mul(2, ConstPi), 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

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2019-06-18 07:49:59.356594 UTC