DLMF:1.14.E9 (Q501)

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DLMF:1.14.E9
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    Statements

    test
    ℱ c ⁡ ( f ) ⁡ ( x ) = ℱ c ⁡ f ⁡ ( x ) = 2 π ⁢ ∫ 0 ∞ f ⁢ ( t ) ⁢ cos ⁡ ( x ⁢ t ) ⁢ d t , Fourier-cosine-transform 𝑓 𝑥 Fourier-cosine-transform 𝑓 𝑥 2 𝜋 subscript superscript 0 𝑓 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{F}_{\mskip-3.0mu c}\left(f\right)\left(x% \right)=\mathscr{F}_{\mskip-3.0mu c}\mskip-1.0mu f\mskip 3.0mu \left(x\right)=% \sqrt{\frac{2}{\pi}}\int^{\infty}_{0}f(t)\cos\left(xt\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.14.E9
    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.m2afdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    Q10888
    test
    F c ⁢ ( x ) subscript 𝐹 𝑐 𝑥 {\displaystyle{\displaystyle F_{c}(x)}}
    xml-id
    C1.S14.XMD4.m1dec
    0 references
     
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