DLMF:1.14.E49 (Q541)

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DLMF:1.14.E49
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    test
    lim t → 0 + ⁡ 𝒮 ⁡ f ⁡ ( - σ - i ⁢ t ) - 𝒮 ⁡ f ⁡ ( - σ + i ⁢ t ) 2 ⁢ π ⁢ i = 1 2 ⁢ ( f ⁢ ( σ + ) + f ⁢ ( σ - ) ) , subscript → 𝑡 limit-from 0 Stieltjes-transform 𝑓 𝜎 𝑖 𝑡 Stieltjes-transform 𝑓 𝜎 𝑖 𝑡 2 𝜋 𝑖 1 2 𝑓 limit-from 𝜎 𝑓 limit-from 𝜎 {\displaystyle{\displaystyle\lim_{t\to 0+}\frac{\mathcal{S}\mskip-3.0mu f% \mskip 3.0mu \left(-\sigma-it\right)-\mathcal{S}\mskip-3.0mu f\mskip 3.0mu % \left(-\sigma+it\right)}{2\pi i}=\tfrac{1}{2}(f(\sigma+)+f(\sigma-)),}}
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    DLMF id
    DLMF:1.14.E49
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