DLMF:2.6.E8 (Q833)

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DLMF:2.6.E8
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    Statements

    test
    𝒮 ⁡ f ⁡ ( z ) = ∫ 0 ∞ f ⁢ ( t ) t + z ⁢ d t . Stieltjes-transform 𝑓 𝑧 superscript subscript 0 𝑓 𝑡 𝑡 𝑧 𝑡 {\displaystyle{\displaystyle\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(z% \right)=\int_{0}^{\infty}\frac{f(t)}{t+z}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:2.6.E8
    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.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1dec
    0 references
     
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