DLMF:2.5.E4 (Q780)

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DLMF:2.5.E4
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    Statements

    Defining formula
    ℳ ⁡ I ⁡ ( z ) = ℳ ⁡ f ⁡ ( 1 - z ) ⁢ ℳ ⁡ h ⁡ ( z ) . Mellin-transform 𝐼 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform ℎ 𝑧 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu I\mskip 3.0mu \left(z% \right)=\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).}}
    0 references
    DLMF id
    DLMF:2.5.E4
    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.m2abdec
    0 references
    Q10992
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S5.XMD1.m1cdec
    0 references
    Q10994
    Defining formula
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1adec
    0 references
    Q10995
    Defining formula
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD6.m1adec
    0 references
     
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