Fungrim entry: 4e4e0f

$\Gamma\!\left(z\right) = \int_{0}^{\infty} {t}^{z - 1} {e}^{-t} \, dt$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(z\right) > 0$
TeX:
\Gamma\!\left(z\right) = \int_{0}^{\infty} {t}^{z - 1} {e}^{-t} \, dt

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(z\right) > 0
Definitions:
Fungrim symbol Notation Short description
GammaFunction$\Gamma\!\left(z\right)$ Gamma function
Integral$\int_{a}^{b} f\!\left(x\right) \, dx$ Integral
Pow${a}^{b}$ Power
Exp${e}^{z}$ Exponential function
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}\!\left(z\right)$ Real part
Source code for this entry:
Entry(ID("4e4e0f"),
Formula(Equal(GammaFunction(z), Integral(Mul(Pow(t, Sub(z, 1)), Exp(Neg(t))), Tuple(t, 0, Infinity)))),
Variables(z),
Assumptions(And(Element(z, CC), Greater(Re(z), 0))))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC