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Sinc function

576 bytes added, 18:41, 19 December 2011
Integration
<math>\int_{-\infty}^\infty \operatorname{sinc} x \, dx = \pi</math>
 
===Second antiderivative===
 
The second antiderivative is:
 
<math>\int (\int \operatorname{sinc} x \, dx) \, dx = x \operatorname{Si}(x) + \cos x + C_1x + C_0</math>
 
To obtain this, we use [[integration by parts]] to integrate the function <math>\operatorname{Si}(x)</math>.
 
===Higher antiderivatives===
 
Higher antiderivatives of the sinc function can be computed in the same manner using [[integration by parts]]. Up to the arbitrary polynomial additive, the antiderivative is expressible as a polynomial linear combination of <math>\operatorname{Si}, \sin, \cos</math>.
==Taylor series and power series==
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