DLMF:5.12.E5 (Q2150)

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DLMF:5.12.E5
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    Statements

    test
    ∫ 0 π / 2 ( cos ⁡ t ) a - 1 ⁢ cos ⁡ ( b ⁢ t ) ⁢ d t = π 2 a ⁢ 1 a ⁢ B ⁡ ( 1 2 ⁢ ( a + b + 1 ) , 1 2 ⁢ ( a - b + 1 ) ) , superscript subscript 0 𝜋 2 superscript 𝑡 𝑎 1 𝑏 𝑡 𝑡 𝜋 superscript 2 𝑎 1 𝑎 Euler-Beta 1 2 𝑎 𝑏 1 1 2 𝑎 𝑏 1 {\displaystyle{\displaystyle\int_{0}^{\pi/2}(\cos t)^{a-1}\cos\left(bt\right)% \mathrm{d}t=\frac{\pi}{2^{a}}\frac{1}{a\mathrm{B}\left(\frac{1}{2}(a+b+1),% \frac{1}{2}(a-b+1)\right)},}}
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    DLMF id
    DLMF:5.12.E5
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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