Fungrim entry: a0ca3e

\Gamma\!\left(x\right) \lt {\left(2 \pi\right)}^{1 / 2} {x}^{x - 1 / 2} {e}^{-x} \exp\!\left(\frac{1}{12 x}\right)

Assumptions:

x \in \left(0, \infty\right)

TeX:

\Gamma\!\left(x\right) \lt {\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
`GammaFunction`	$\Gamma\!\left(z\right)$	Gamma function
`Pow`	${a}^{b}$	Power
`ConstPi`	$\pi$	The constant pi (3.14...)
`Exp`	${e}^{z}$	Exponential function
`OpenInterval`	$\left(a, b\right)$	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))))

Topics using this entry

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

2019-06-18 07:49:59.356594 UTC