Formula:509

Digital Library of Mathematical Functions ID 1.14.E48

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{m}}{{\mathrm{d}s}^{m}}\mathcal{S}\mskip-3.0mu f\mskip 3.0mu \left(s\right)=(-1)^{m}m!\int^{\infty}_{0}\frac{f(t)\mathrm{d}t}{(s+t)^{m+1}},}}$

Constraint(s)

${\displaystyle{\displaystyle m=0,1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{S}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Stieltjes transform
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
 

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