Formula:8130

Digital Library of Mathematical Functions ID 24.4.E24

${\displaystyle{\displaystyle B_{n}\left(mx\right)=m^{n}B_{n}\left(x\right)+n\sum_{k=1}^{n}\sum_{j=0}^{k-1}(-1)^{j}{n\choose k}\*\left(\sum_{r=1}^{m-1}\frac{e^{2\pi i(k-j)r/m}}{(1-e^{2\pi ir/m})^{n}}\right)(j+mx)^{n-1},}}$

Constraint(s)

${\displaystyle{\displaystyle m=2,3,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$:
• ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle j}}$: integer
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle x}}$: real or complex
 

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