https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Sine_integralSine integral - Revision history2026-08-08T00:49:24ZRevision history for this page on the wikiMediaWiki 1.41.2https://companal.subwiki.org/w/index.php?title=Sine_integral&diff=480&oldid=prevVipul: 1 revision2008-05-18T19:18:43Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://companal.subwiki.org/w/index.php?title=Sine_integral&diff=479&oldid=prevVipul: New page: {{particular entire function}} ==Definition== The '''sine integral''' is defined as the antiderivative of the sinc function taking the value 0 at 0. Denoted <math>\operatorname{Si}</...2008-04-27T21:34:07Z<p>New page: {{particular entire function}} ==Definition== The '''sine integral''' is defined as the antiderivative of the <a href="/wiki/Sinc_function" title="Sinc function">sinc function</a> taking the value 0 at 0. Denoted <math>\operatorname{Si}</...</p>
<p><b>New page</b></p><div>{{particular entire function}}<br />
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==Definition==<br />
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The '''sine integral''' is defined as the antiderivative of the [[sinc function]] taking the value 0 at 0. Denoted <math>\operatorname{Si}</math>, it is defined as:<br />
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<math>\operatorname{Si}(z_0) := \int_0^{z_0} \operatorname{sinc}(z) \, dz</math><br />
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The integration could be done over ''any'' piecewise smooth path from <math>0</math> to <math>z_0</math>: all such integrals yield the same value because of the [[homotopy-invariance formulation of Cauchy's theorem]], and the fact that <math>\mathbb{C}</math> is simply connected.</div>Vipul