DLMF:2.5.E48 (Q824): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2afdec

Revision as of 17:09, 1 January 2020

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DLMF:2.5.E48
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    Statements

    h ( ζ ) ( - ln ζ ) k = 0 ζ k k ! + k = 0 ψ ( k + 1 ) ζ k k ! , asymptotic-expansion Laplace-transform 𝜁 𝜁 superscript subscript 𝑘 0 superscript 𝜁 𝑘 𝑘 superscript subscript 𝑘 0 digamma 𝑘 1 superscript 𝜁 𝑘 𝑘 {\displaystyle{\displaystyle\mathscr{L}\mskip-3.0mu h\mskip 3.0mu \left(\zeta% \right)\sim(-\ln\zeta)\sum_{k=0}^{\infty}\frac{\zeta^{k}}{k!}+\sum_{k=0}^{% \infty}\psi\left(k+1\right)\frac{\zeta^{k}}{k!},}}
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    DLMF:2.5.E48
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    ζ 0 + 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}
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    ( f ) ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E17.m2aedec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11acdec
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    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2abdec
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2afdec
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