Fungrim entry: a26ac7

\Gamma(z) = \exp\!\left(\log \Gamma(z)\right)

Assumptions:

z \in \mathbb{C} \setminus \{0, -1, \ldots\}

TeX:

\Gamma(z) = \exp\!\left(\log \Gamma(z)\right)

z \in \mathbb{C} \setminus \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`Gamma`	$\Gamma(z)$	Gamma function
`Exp`	${e}^{z}$	Exponential function
`LogGamma`	$\log \Gamma(z)$	Logarithmic gamma function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("a26ac7"),
    Formula(Equal(Gamma(z), Exp(LogGamma(z)))),
    Variables(z),
    Assumptions(And(Element(z, SetMinus(CC, ZZLessEqual(0))))))

Topics using this entry

2021-03-15 19:12:00.328586 UTC