Fungrim entry: 4e4e0f

\Gamma(z) = \int_{0}^{\infty} {t}^{z - 1} {e}^{-t} \, dt

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0

TeX:

\Gamma(z) = \int_{0}^{\infty} {t}^{z - 1} {e}^{-t} \, dt

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(z) > 0

Definitions:

Fungrim symbol	Notation	Short description
`Gamma`	$\Gamma(z)$	Gamma function
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Pow`	${a}^{b}$	Power
`Exp`	${e}^{z}$	Exponential function
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}(z)$	Real part

Source code for this entry:

Entry(ID("4e4e0f"),
    Formula(Equal(Gamma(z), Integral(Mul(Pow(t, Sub(z, 1)), Exp(Neg(t))), For(t, 0, Infinity)))),
    Variables(z),
    Assumptions(And(Element(z, CC), Greater(Re(z), 0))))

Topics using this entry

Gamma function

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