Fungrim entry: 774d37

\log \Gamma\!\left(z + 1\right) = \log \Gamma\!\left(z\right) + \log\!\left(z\right)

Assumptions:

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

TeX:

\log \Gamma\!\left(z + 1\right) = \log \Gamma\!\left(z\right) + \log\!\left(z\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`LogGamma`	$\log \Gamma\!\left(z\right)$	Logarithmic gamma function
`Log`	$\log\!\left(z\right)$	Natural logarithm
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("774d37"),
    Formula(Equal(LogGamma(Add(z, 1)), Add(LogGamma(z), Log(z)))),
    Variables(z),
    Assumptions(And(Element(z, SetMinus(CC, ZZLessEqual(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.

2019-06-18 07:49:59.356594 UTC