DLMF:1.8.E15 (Q269)

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DLMF:1.8.E15
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    Statements

    Defining formula
    1 2 ⁢ f ⁢ ( 0 ) + ∑ n = 1 ∞ f ⁢ ( n ) = ∫ 0 ∞ f ⁢ ( x ) ⁢ d x + 2 ⁢ ∑ n = 1 ∞ ∫ 0 ∞ f ⁢ ( x ) ⁢ cos ⁡ ( 2 ⁢ π ⁢ n ⁢ x ) ⁢ d x . 1 2 𝑓 0 subscript superscript 𝑛 1 𝑓 𝑛 subscript superscript 0 𝑓 𝑥 𝑥 2 subscript superscript 𝑛 1 subscript superscript 0 𝑓 𝑥 2 𝜋 𝑛 𝑥 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}f(0)+\sum^{\infty}_{n=1}f(n)=\int^{% \infty}_{0}f(x)\mathrm{d}x+2\sum^{\infty}_{n=1}\int^{\infty}_{0}f(x)\cos\left(% 2\pi nx\right)\mathrm{d}x.}}
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    DLMF id
    DLMF:1.8.E15
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
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