Fungrim entry: e9f966

\mathrm{B}\!\left(a, b\right) = \mathrm{B}\!\left(a + 1, b\right) + \mathrm{B}\!\left(a, b + 1\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) = \mathrm{B}\!\left(a + 1, b\right) + \mathrm{B}\!\left(a, b + 1\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
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("e9f966"),
    Formula(Equal(BetaFunction(a, b), Add(BetaFunction(Add(a, 1), b), BetaFunction(a, Add(b, 1))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))))))

Topics using this entry

Beta function