DLMF:1.8.E12 (Q266): Difference between revisions

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Property / constraint
 

0 x 2 π 0 𝑥 2 𝜋 {\displaystyle{\displaystyle 0\leq x\leq 2\pi}}

0\leq x\leq 2\pi
Property / constraint: 0 x 2 π 0 𝑥 2 𝜋 {\displaystyle{\displaystyle 0\leq x\leq 2\pi}} / rank
 
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Revision as of 15:48, 30 December 2019

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DLMF:1.8.E12
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    0 x ( f ( t ) - 1 2 a 0 ) d t = n = 1 a n sin ( n x ) + b n ( 1 - cos ( n x ) ) n , subscript superscript 𝑥 0 𝑓 𝑡 1 2 subscript 𝑎 0 𝑡 subscript superscript 𝑛 1 subscript 𝑎 𝑛 𝑛 𝑥 subscript 𝑏 𝑛 1 𝑛 𝑥 𝑛 {\displaystyle{\displaystyle\int^{x}_{0}(f(t)-\tfrac{1}{2}a_{0})\mathrm{d}t=% \sum^{\infty}_{n=1}\frac{a_{n}\sin\left(nx\right)+b_{n}(1-\cos\left(nx\right))% }{n},}}
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    0 x 2 π 0 𝑥 2 𝜋 {\displaystyle{\displaystyle 0\leq x\leq 2\pi}}
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