DLMF:2.6.E25 (Q850)

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DLMF:2.6.E25
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    Statements

    test
    lim ε → 0 ⁡ ⟨ f , ϕ ε ⟩ = 𝒮 ⁡ f ⁡ ( z ) , subscript → 𝜀 0 distribution 𝑓 subscript italic-ϕ 𝜀 Stieltjes-transform 𝑓 𝑧 {\displaystyle{\displaystyle\lim_{\varepsilon\to 0}\left\langle f,\phi_{% \varepsilon}\right\rangle=\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z\right)% ,}}
    0 references
    DLMF id
    DLMF:2.6.E25
    0 references
    Symbols used
    Stieltjes transform
    test
    𝒮 ⁡ ( f ) ⁡ ( s ) Stieltjes-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    xml-id
    C1.S14.E47.m2aadec
    0 references
    Q10905
    test
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5ajdec
    0 references
    Q11026
    test
    ε 𝜀 {\displaystyle{\displaystyle\varepsilon}}
    xml-id
    C2.S6.XMD11.m1cdec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1hdec
    0 references
     
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