DLMF:2.5.E6 (Q782)

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DLMF:2.5.E6
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    Statements

    Defining formula
    I ⁢ ( x ) = ∑ d < ℜ ⁡ z < c res ⁡ [ x - z ⁢ ℳ ⁡ f ⁡ ( 1 - z ) ⁢ ℳ ⁡ h ⁡ ( z ) ] + E ⁢ ( x ) , 𝐼 𝑥 subscript 𝑑 𝑧 𝑐 residue delimited-[] superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform ℎ 𝑧 𝐸 𝑥 {\displaystyle{\displaystyle I(x)=\sum\limits_{d<\Re z<c}\Residue\left[x^{-z}% \mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu % h\mskip 3.0mu \left(z\right)\right]+E(x),}}
    0 references
    DLMF id
    DLMF:2.5.E6
    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.m2addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
     
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