Fungrim entry: fd0e48

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

Assumptions:

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

TeX:

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

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; a + b \notin \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b + c \notin \{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("fd0e48"),
    Formula(Equal(Mul(BetaFunction(a, b), BetaFunction(Add(a, b), c)), Mul(BetaFunction(b, c), BetaFunction(a, Add(b, c))))),
    Variables(a, b, c),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))), Element(c, SetMinus(CC, ZZLessEqual(0))), NotElement(Add(a, b), ZZLessEqual(0)), NotElement(Add(b, c), ZZLessEqual(0)))))

Topics using this entry

Beta function