DLMF:1.14.E11 (Q503)

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DLMF:1.14.E11
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    Statements

    Defining formula
    1 2 ⁢ ( f ⁢ ( u + ) + f ⁢ ( u - ) ) = 2 π ⁢ ∫ 0 ∞ F c ⁢ ( x ) ⁢ cos ⁡ ( u ⁢ x ) ⁢ d x , 1 2 𝑓 limit-from 𝑢 𝑓 limit-from 𝑢 2 𝜋 subscript superscript 0 subscript 𝐹 𝑐 𝑥 𝑢 𝑥 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}(f(u+)+f(u-))=\sqrt{\frac{2}{\pi}}\int% ^{\infty}_{0}F_{c}(x)\cos\left(ux\right)\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:1.14.E11
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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