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Fungrim entry: bdea17

(a+b)B ⁣(a+1,b)=aB ⁣(a,b)\left(a + b\right) \mathrm{B}\!\left(a + 1, b\right) = a \mathrm{B}\!\left(a, b\right)
Assumptions:a∈C∖{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\}
TeX:
\left(a + b\right) \mathrm{B}\!\left(a + 1, b\right) = a \mathrm{B}\!\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
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZ≤n\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("bdea17"),
    Formula(Equal(Mul(Add(a, b), BetaFunction(Add(a, 1), b)), Mul(a, BetaFunction(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, 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