DLMF:2.5.E47 (Q823): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Mellin transform / rank
 
Normal rank
Property / Symbols used: Mellin transform / qualifier
 
test:

ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}

\Mellintrans@{\NVar{f}}@{\NVar{s}}
Property / Symbols used: Mellin transform / qualifier
 
xml-id: C1.S14.E32.m2asdec

Revision as of 16:08, 1 January 2020

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DLMF:2.5.E47
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    Statements

    test
    res z = 1 ⁡ [ - ζ z - 1 ⁢ Γ ⁡ ( 1 - z ) ⁢ ℳ ⁡ h 2 ⁡ ( z ) ] = ( - ln ⁡ ζ - γ ) - ℳ ⁡ h 1 ⁡ ( 1 ) , subscript residue 𝑧 1 delimited-[] superscript 𝜁 𝑧 1 Euler-Gamma 1 𝑧 Mellin-transform subscript ℎ 2 𝑧 𝜁 Mellin-transform subscript ℎ 1 1 {\displaystyle{\displaystyle\Residue_{z=1}\left[-\zeta^{z-1}\Gamma\left(1-z% \right)\mathscr{M}\mskip-3.0mu h_{2}\mskip 3.0mu \left(z\right)\right]=\left(-% \ln\zeta-\gamma\right)-\mathscr{M}\mskip-3.0mu h_{1}\mskip 3.0mu \left(1\right% ),}}
    0 references
    DLMF id
    DLMF:2.5.E47
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
    0 references
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    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.m2asdec
    0 references
     
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