Formula:965

Digital Library of Mathematical Functions ID 2.10.E7

${\displaystyle{\displaystyle\sum_{j=1}^{n-1}j^{\alpha}\sim\zeta\left(-\alpha\right)+\frac{n^{\alpha+1}}{\alpha+1}\sum_{s=0}^{\infty}\genfrac{(}{)}{0.0pt}{}{\alpha+1}{s}\frac{B_{s}}{n^{s}},}}$

Constraint(s)

${\displaystyle{\displaystyle n\to\infty}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle n}}$: integer
 

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