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Fungrim entry: 542cf7

B ⁣(a,b)=01ta1(1t)b1dt\mathrm{B}\!\left(a, b\right) = \int_{0}^{1} {t}^{a - 1} {\left(1 - t\right)}^{b - 1} \, dt
Assumptions:aCandbCandRe ⁣(a)>0andRe ⁣(b)>0a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(a\right) > 0 \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(b\right) > 0
TeX:
\mathrm{B}\!\left(a, b\right) = \int_{0}^{1} {t}^{a - 1} {\left(1 - t\right)}^{b - 1} \, dt

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(a\right) > 0 \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(b\right) > 0
Definitions:
Fungrim symbol Notation Short description
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
Integralabf ⁣(x)dx\int_{a}^{b} f\!\left(x\right) \, dx Integral
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
Source code for this entry:
Entry(ID("542cf7"),
    Formula(Equal(BetaFunction(a, b), Integral(Mul(Pow(t, Sub(a, 1)), Pow(Sub(1, t), Sub(b, 1))), Tuple(t, 0, 1)))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC), Greater(Re(a), 0), Greater(Re(b), 0))))

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2019-08-25 15:30:03.056001 UTC