DLMF:2.5.E1 (Q777)

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DLMF:2.5.E1
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    Statements

    Defining formula
    ℳ ⁡ f ⁡ ( z ) = ∫ 0 ∞ t z - 1 ⁢ f ⁢ ( t ) ⁢ d t , Mellin-transform 𝑓 𝑧 superscript subscript 0 superscript 𝑡 𝑧 1 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z% \right)=\int_{0}^{\infty}t^{z-1}f(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.5.E1
    0 references
    Symbols used
    Mellin transform
    Defining formula
    ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E32.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q10992
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S5.XMD1.m1dec
    0 references
     
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