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

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Property / constraint
 

ζ → 0 + → 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}

\zeta\to 0+
Property / constraint: ζ → 0 + → 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Laplace transform / rank
 
Normal rank
Property / Symbols used: Laplace transform / qualifier
 
test:

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

\Laplacetrans@{\NVar{f}}@{\NVar{s}}
Property / Symbols used: Laplace transform / qualifier
 
xml-id: C1.S14.E17.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11acdec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
test:

ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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
Property / Symbols used
 
Property / Symbols used: Q11005 / rank
 
Normal rank
Property / Symbols used: Q11005 / qualifier
 
test:

h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}

h(x)
Property / Symbols used: Q11005 / qualifier
 
xml-id: C2.S5.XMD16.m1sdec

Latest revision as of 16:09, 1 January 2020

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DLMF:2.5.E48
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    Statements

    test
    ℒ ⁡ h ⁡ ( ζ ) ∼ ( - ln ⁡ ζ ) ⁢ ∑ k = 0 ∞ ζ k k ! + ∑ k = 0 ∞ ψ ⁡ ( k + 1 ) ⁢ ζ k k ! , asymptotic-expansion Laplace-transform ℎ 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!},}}
    0 references
    DLMF id
    DLMF:2.5.E48
    0 references
    constraint
    ζ → 0 + → 𝜁 limit-from 0 {\displaystyle{\displaystyle\zeta\to 0+}}
    0 references
    Symbols used
    Laplace transform
    test
    ℒ ⁡ ( f ) ⁡ ( s ) Laplace-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{L}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E17.m2aedec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2abdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2afdec
    0 references
    Q11005
    test
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD16.m1sdec
    0 references
     
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