DLMF:6.16.E2 (Q2311): Difference between revisions

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Latest revision as of 01:35, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:6.16.E2	No description defined

Statements

Defining formula

{\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),}}

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DLMF:6.16.E2

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Symbols defined

partial sum (locally)

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}

C6.S2.E9.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C6.S1.XMD1.m1adec

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Defining formula

{\displaystyle{\displaystyle n}}

C6.S1.XMD3.m1dec

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remainder term (locally)

Defining formula

{\displaystyle{\displaystyle R_{n}(x)}}

C6.S16.XMD2.m1dec

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