DLMF:2.5.E2 (Q778)

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DLMF:2.5.E2
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    Statements

    test
    f ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ t - z ⁢ ℳ ⁡ f ⁡ ( z ) ⁢ d z , 𝑓 𝑡 1 2 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 superscript 𝑡 𝑧 Mellin-transform 𝑓 𝑧 𝑧 {\displaystyle{\displaystyle f(t)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}% t^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z\right)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:2.5.E2
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    Symbols used
    Mellin transform
    test
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2aadec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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