Fungrim entry: 888581

\mathrm{B}\!\left(a, b\right) = \frac{\Gamma(a) \Gamma(b)}{\Gamma\!\left(a + b\right)}

Assumptions:

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\}

TeX:

\mathrm{B}\!\left(a, b\right) = \frac{\Gamma(a) \Gamma(b)}{\Gamma\!\left(a + b\right)}

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`BetaFunction`	$\mathrm{B}\!\left(a, b\right)$	Beta function
`Gamma`	$\Gamma(z)$	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("888581"),
    Formula(Equal(BetaFunction(a, b), Div(Mul(Gamma(a), Gamma(b)), Gamma(Add(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))))))

Topics using this entry

Gamma function
Beta function