DLMF:1.8.E13 (Q267)

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DLMF:1.8.E13
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    Defining formula
    1 π ⁢ ∫ - π π f ⁢ ( x ) ⁢ g ⁢ ( x ) ⁢ d x = 1 2 ⁢ a 0 ⁢ a 0 ′ + ∑ n = 1 ∞ ( a n ⁢ a n ′ + b n ⁢ b n ′ ) , 1 𝜋 subscript superscript 𝜋 𝜋 𝑓 𝑥 𝑔 𝑥 𝑥 1 2 subscript 𝑎 0 subscript superscript 𝑎 ′ 0 subscript superscript 𝑛 1 subscript 𝑎 𝑛 subscript superscript 𝑎 ′ 𝑛 subscript 𝑏 𝑛 subscript superscript 𝑏 ′ 𝑛 {\displaystyle{\displaystyle\frac{1}{\pi}\int^{\pi}_{-\pi}f(x)g(x)\mathrm{d}x=% \tfrac{1}{2}a_{0}a^{\prime}_{0}+\sum^{\infty}_{n=1}(a_{n}a^{\prime}_{n}+b_{n}b% ^{\prime}_{n}),}}
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    DLMF id
    DLMF:1.8.E13
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