https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Integral_formulaIntegral formula - Revision history2026-04-17T15:09:40ZRevision history for this page on the wikiMediaWiki 1.41.2https://companal.subwiki.org/w/index.php?title=Integral_formula&diff=252&oldid=prevVipul: 2 revisions2008-05-18T19:13:53Z<p>2 revisions</p>
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</td></tr></table>Vipulhttps://companal.subwiki.org/w/index.php?title=Integral_formula&diff=251&oldid=prevVipul: /* Examples */2008-05-01T19:47:52Z<p><span dir="auto"><span class="autocomment">Examples</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Examples==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Examples==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[Euler's integral formula for gamma function]]: This formula describes the gamma function in the [[right half-plane]], even though the gamma function is actually defined on the complement of the set of non-positive integers.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [[Euler's integral formula for gamma function]]: This formula describes the <ins style="font-weight: bold; text-decoration: none;">[[</ins>gamma function<ins style="font-weight: bold; text-decoration: none;">]] </ins>in the [[right half-plane]], even though the gamma function is actually defined on the complement of the set of non-positive integers.</div></td></tr>
</table>Vipulhttps://companal.subwiki.org/w/index.php?title=Integral_formula&diff=250&oldid=prevVipul: New page: ==Definition== An '''integral formula''' or '''integral representation''' for a holomorphic function or meromorphic function <math>f: U \to \mathbb{C}</math> is defined as a pair ...2008-05-01T19:47:13Z<p>New page: ==Definition== An '''integral formula''' or '''integral representation''' for a <a href="/wiki/Holomorphic_function" title="Holomorphic function">holomorphic function</a> or <a href="/wiki/Meromorphic_function" title="Meromorphic function">meromorphic function</a> <math>f: U \to \mathbb{C}</math> is defined as a pair ...</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
An '''integral formula''' or '''integral representation''' for a [[holomorphic function]] or [[meromorphic function]] <math>f: U \to \mathbb{C}</math> is defined as a pair <math>(F,\gamma)</math> where <math>F</math> is a holomorphic function of two complex variables, and <math>\gamma</math> is a curve in <math>\mathbb{C}</math>, such that we have the identity:<br />
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<math>f(z) = \int_\gamma F(z,w) \, dw</math><br />
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on a nonempty open subset of <math>U</math>. In fact, equality holds wherever both sides make sense.<br />
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==Examples==<br />
<br />
* [[Euler's integral formula for gamma function]]: This formula describes the gamma function in the [[right half-plane]], even though the gamma function is actually defined on the complement of the set of non-positive integers.</div>Vipul