Formula:3009

Digital Library of Mathematical Functions ID 6.16.E2

${\displaystyle{\displaystyle S_{n}(x)=\sum_{k=0}^{n-1}\frac{\sin\left((2k+1)x\right)}{2k+1}=\frac{1}{2}\int_{0}^{x}\frac{\sin\left(2nt\right)}{\sin t}\mathrm{d}t=\tfrac{1}{2}\mathrm{Si}\left(2nx\right)+R_{n}(x),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}$: sine integral
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle R_{n}(x)}}$: remainder term (locally)
 

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