DLMF:1.14.E48 (Q540)

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DLMF:1.14.E48
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    Statements

    Defining formula
    d m d s m ⁡ 𝒮 ⁡ f ⁡ ( s ) = ( - 1 ) m ⁢ m ! ⁢ ∫ 0 ∞ f ⁢ ( t ) ⁢ d t ( s + t ) m + 1 , derivative 𝑠 𝑚 Stieltjes-transform 𝑓 𝑠 superscript 1 𝑚 𝑚 subscript superscript 0 𝑓 𝑡 𝑡 superscript 𝑠 𝑡 𝑚 1 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{m}}{{\mathrm{d}s}^{m}}\mathcal% {S}\mskip-3.0mu f\mskip 3.0mu \left(s\right)=(-1)^{m}m!\int^{\infty}_{0}\frac{% f(t)\mathrm{d}t}{(s+t)^{m+1}},}}
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    DLMF id
    DLMF:1.14.E48
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