Formula:8556

Digital Library of Mathematical Functions ID 26.8.E35

${\displaystyle{\displaystyle\sum_{j=0}^{n}j^{k}=\sum_{j=0}^{k}j!S\left(k,j\right)\genfrac{(}{)}{0.0pt}{}{n+1}{j+1},}}$

Symbols List

• ${\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}$:
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle j}}$: nonnegative integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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