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Fungrim entry: fd0e48

B ⁣(a,b)B ⁣(a+b,c)=B ⁣(b,c)B ⁣(a,b+c)\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:aC{0,1,}  and  bC{0,1,}  and  cC{0,1,}  and  a+b{0,1,}  and  b+c{0,1,}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\}
\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\}
Fungrim symbol Notation Short description
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    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)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC