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	<id>https://companal.subwiki.org/w/index.php?action=history&amp;feed=atom&amp;title=Reciprocal_of_gamma_function</id>
	<title>Reciprocal of gamma function - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://companal.subwiki.org/w/index.php?action=history&amp;feed=atom&amp;title=Reciprocal_of_gamma_function"/>
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	<updated>2026-04-18T17:52:43Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.41.2</generator>
	<entry>
		<id>https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=389&amp;oldid=prev</id>
		<title>Vipul: 3 revisions</title>
		<link rel="alternate" type="text/html" href="https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=389&amp;oldid=prev"/>
		<updated>2008-05-18T19:17:47Z</updated>

		<summary type="html">&lt;p&gt;3 revisions&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:17, 18 May 2008&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;en&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
	<entry>
		<id>https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=388&amp;oldid=prev</id>
		<title>Vipul: /* Definition */</title>
		<link rel="alternate" type="text/html" href="https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=388&amp;oldid=prev"/>
		<updated>2008-05-01T20:23:51Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Definition&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:23, 1 May 2008&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l10&quot;&gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &amp;#039;&amp;#039;not&amp;#039;&amp;#039; a simple pole of the gamma function. If &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is a simple pole, it sends &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; to 0.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &amp;#039;&amp;#039;not&amp;#039;&amp;#039; a simple pole of the gamma function. If &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is a simple pole, it sends &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; to 0.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;===In terms of Hankel&#039;s loop contour===&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Let &amp;lt;math&amp;gt;\gamma&amp;lt;/math&amp;gt; denote [[Hankel&#039;s loop contour]]. The reciprocal of the gamma function is then defined as:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;z \mapsto \int_\gamma e^{-w} w^{-z} \, dw&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
	<entry>
		<id>https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=387&amp;oldid=prev</id>
		<title>Vipul at 20:15, 1 May 2008</title>
		<link rel="alternate" type="text/html" href="https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=387&amp;oldid=prev"/>
		<updated>2008-05-01T20:15:34Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:15, 1 May 2008&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot;&gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;z \mapsto \frac{1}{\Gamma(z)}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;z \mapsto \frac{1}{\Gamma(z)}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &#039;&#039;not&#039;&#039; a simple pole of the gamma function. If &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is a simple pole, it sends &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the residue at &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt;&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &#039;&#039;not&#039;&#039; a simple pole of the gamma function. If &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is a simple pole, it sends &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;0&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
	<entry>
		<id>https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=386&amp;oldid=prev</id>
		<title>Vipul: New page: {{particular entire function}}  ==Definition==  ===As the reciprocal of the gamma function===  It is defined as:  &lt;math&gt;z \mapsto \frac{1}{\Gamma(z)}&lt;/math&gt;  if &lt;math&gt;z&lt;/math&gt; is &#039;&#039;not&#039;&#039; a...</title>
		<link rel="alternate" type="text/html" href="https://companal.subwiki.org/w/index.php?title=Reciprocal_of_gamma_function&amp;diff=386&amp;oldid=prev"/>
		<updated>2008-05-01T20:10:33Z</updated>

		<summary type="html">&lt;p&gt;New page: {{particular entire function}}  ==Definition==  ===As the reciprocal of the gamma function===  It is defined as:  &amp;lt;math&amp;gt;z \mapsto \frac{1}{\Gamma(z)}&amp;lt;/math&amp;gt;  if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &amp;#039;&amp;#039;not&amp;#039;&amp;#039; a...&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{particular entire function}}&lt;br /&gt;
&lt;br /&gt;
==Definition==&lt;br /&gt;
&lt;br /&gt;
===As the reciprocal of the gamma function===&lt;br /&gt;
&lt;br /&gt;
It is defined as:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;z \mapsto \frac{1}{\Gamma(z)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
if &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is &amp;#039;&amp;#039;not&amp;#039;&amp;#039; a simple pole of the gamma function. If &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is a simple pole, it sends &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; to the residue at &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt;.&lt;/div&gt;</summary>
		<author><name>Vipul</name></author>
	</entry>
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