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Fungrim entry: 4e4e0f

Γ ⁣(z)=∫0∞tz−1e−t dt\Gamma\!\left(z\right) = \int_{0}^{\infty} {t}^{z - 1} {e}^{-t} \, dt
Assumptions:z∈C and⁡ Re⁡ ⁣(z)>0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(z\right) \gt 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) \gt 0
Definitions:
Fungrim symbol Notation Short description
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
Powab{a}^{b} Power
Expez{e}^{z} Exponential function
Infinity∞\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe⁡ ⁣(z)\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.

2019-06-18 07:49:59.356594 UTC