DLMF:2.6.E24 (Q849): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
test:

Λ , ϕ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}

\intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
Property / Symbols used: Q10905 / qualifier
 
xml-id: C1.S16.SS1.p5.m5aidec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11026 / rank
 
Normal rank
Property / Symbols used: Q11026 / qualifier
 
test:

ε 𝜀 {\displaystyle{\displaystyle\varepsilon}}

\varepsilon
Property / Symbols used: Q11026 / qualifier
 
xml-id: C2.S6.XMD11.m1bdec

Latest revision as of 16:12, 1 January 2020

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DLMF:2.6.E24
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    Statements

    lim ε 0 t - s - 1 , ϕ ε = ( - 1 ) s + 1 z s + 1 k = 1 s 1 k + ( - 1 ) s z s + 1 ln z , subscript 𝜀 0 distribution superscript 𝑡 𝑠 1 subscript italic-ϕ 𝜀 superscript 1 𝑠 1 superscript 𝑧 𝑠 1 superscript subscript 𝑘 1 𝑠 1 𝑘 superscript 1 𝑠 superscript 𝑧 𝑠 1 𝑧 {\displaystyle{\displaystyle\lim_{\varepsilon\to 0}\left\langle t^{-s-1},\phi_% {\varepsilon}\right\rangle=\frac{(-1)^{s+1}}{z^{s+1}}\sum_{k=1}^{s}\frac{1}{k}% +\frac{(-1)^{s}}{z^{s+1}}\ln z,}}
    0 references
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    Λ , ϕ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    C1.S16.SS1.p5.m5aidec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    ε 𝜀 {\displaystyle{\displaystyle\varepsilon}}
    C2.S6.XMD11.m1bdec
    0 references