DLMF:5.12.E2 (Q2147)

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DLMF:5.12.E2
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    Statements

    test
    ∫ 0 π / 2 sin 2 ⁢ a - 1 ⁡ θ ⁢ cos 2 ⁢ b - 1 ⁡ θ ⁢ d θ = 1 2 ⁢ B ⁡ ( a , b ) . superscript subscript 0 𝜋 2 2 𝑎 1 𝜃 2 𝑏 1 𝜃 𝜃 1 2 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\pi/2}{\sin^{2a-1}}\theta{\cos^{2b-1}}% \theta\mathrm{d}\theta=\tfrac{1}{2}\mathrm{B}\left(a,b\right).}}
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    DLMF id
    DLMF:5.12.E2
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    Symbols used
    beta function
    test
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2aadec
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    the ratio of the circumference of a circle to its diameter
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    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
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    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
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    C4.S14.E2.m2adec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
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    C1.S4.SS4.m1aadec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
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    C1.S4.SS4.m3aadec
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    sine function
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    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q11275
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1adec
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    Q11283
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1adec
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