DLMF:1.14.E48 (Q540): Difference between revisions

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

m=0,1,2,\dots
Property / constraint: m = 0 , 1 , 2 , 𝑚 0 1 2 {\displaystyle{\displaystyle m=0,1,2,\dots}} / rank
 
Normal rank

Revision as of 16:50, 30 December 2019

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DLMF:1.14.E48
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    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:1.14.E48
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    m = 0 , 1 , 2 , 𝑚 0 1 2 {\displaystyle{\displaystyle m=0,1,2,\dots}}
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