DLMF:5.12.E1 (Q2146)

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DLMF:5.12.E1
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    Statements

    test
    B ⁡ ( a , b ) = ∫ 0 1 t a - 1 ⁢ ( 1 - t ) b - 1 ⁢ d t = Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) Γ ⁡ ( a + b ) . Euler-Beta 𝑎 𝑏 superscript subscript 0 1 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 1 𝑡 Euler-Gamma 𝑎 Euler-Gamma 𝑏 Euler-Gamma 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(a,b\right)=\int_{0}^{1}t^{a-1}(1-t% )^{b-1}\mathrm{d}t=\frac{\Gamma\left(a\right)\Gamma\left(b\right)}{\Gamma\left% (a+b\right)}.}}
    0 references
    DLMF id
    DLMF:5.12.E1
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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