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DLMF:1.14.E32 - MaRDI portal

DLMF:1.14.E32 (Q493)

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DLMF:1.14.E32
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    Statements

    DLMF defining formula
    ℳ ⁡ ( f ) ⁡ ( s ) = ℳ ⁡ f ⁡ ( s ) = ∫ 0 ∞ x s - 1 ⁢ f ⁢ ( x ) ⁢ d x . Mellin-transform 𝑓 𝑠 Mellin-transform 𝑓 𝑠 subscript superscript 0 superscript 𝑥 𝑠 1 𝑓 𝑥 𝑥 {\displaystyle{\displaystyle\mathscr{M}\left(f\right)\left(s\right)=\mathscr{M% }\mskip-3.0mu f\mskip 3.0mu \left(s\right)=\int^{\infty}_{0}x^{s-1}f(x)\mathrm% {d}x.}}
    0 references
    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1avdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3audec
    0 references
     
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