DLMF:1.14.E12 (Q504)

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DLMF:1.14.E12
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    Statements

    test
    1 2 ⁢ ( f ⁢ ( u + ) + f ⁢ ( u - ) ) = 2 π ⁢ ∫ 0 ∞ F s ⁢ ( x ) ⁢ sin ⁡ ( u ⁢ x ) ⁢ d x . 1 2 𝑓 limit-from 𝑢 𝑓 limit-from 𝑢 2 𝜋 subscript superscript 0 subscript 𝐹 𝑠 𝑥 𝑢 𝑥 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}(f(u+)+f(u-))=\sqrt{\frac{2}{\pi}}\int% ^{\infty}_{0}F_{s}(x)\sin\left(ux\right)\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:1.14.E12
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q10889
    test
    F s ⁢ ( x ) subscript 𝐹 𝑠 𝑥 {\displaystyle{\displaystyle F_{s}(x)}}
    xml-id
    C1.S14.XMD5.m1adec
    0 references
     
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