http://www.convexoptimization.com/wikimization/index.php?action=history&feed=atom&title=Binomial_coefficient 2026-04-24T21:05:58Z Revision history for this page on the wiki MediaWiki 1.11.0 http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3305&oldid=prev 2024-09-17T00:56:17Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 00:56, 17 September 2024</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== full definition, Matlab ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== full definition, Matlab ==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg [336]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg [336]<ins style="color: red; font-weight: bold; text-decoration: none;">.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3304&oldid=prev 2024-09-17T00:55:00Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 00:55, 17 September 2024</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 31:</td> <td colspan="2" class="diff-lineno">Line 31:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==References==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>336. M.J. Kronenburg, [https://arxiv.org/pdf/1105.3689.pdf &quot;The Binomial Coefficient for Negative Arguments&quot;], arXiv:1105.<del style="color: red; font-weight: bold; text-decoration: none;">3689.</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>336. M.J. Kronenburg, [https://arxiv.org/pdf/1105.3689.pdf &quot;The Binomial Coefficient for Negative Arguments&quot;], arXiv:1105.<ins style="color: red; font-weight: bold; text-decoration: none;">3689v2</ins></div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3303&oldid=prev 2024-09-17T00:45:48Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 00:45, 17 September 2024</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== full definition, Matlab ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== full definition, Matlab ==</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg [<ins style="color: red; font-weight: bold; text-decoration: none;">336</ins>]</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[<del style="color: red; font-weight: bold; text-decoration: none;">https://arxiv.org/pdf/1105.3689.pdf</del>]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 30:</td> <td colspan="2" class="diff-lineno">Line 29:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>return</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>return</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/pre&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/pre&gt;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==References==</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>336. M.J. Kronenburg, [https://arxiv.org/pdf/1105.3689.pdf &quot;The Binomial Coefficient for Negative Arguments&quot;], arXiv:1105.3689.</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3258&oldid=prev 2022-03-05T03:08:01Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 03:08, 5 March 2022</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 4:</td> <td colspan="2" class="diff-lineno">Line 4:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[[Image:Binomial.jpg|thumb|right|700px|full binomial coefficient definition including negative argument]]</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;pre&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;pre&gt;</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3239&oldid=prev 2022-01-28T01:18:36Z

<p><span class="autocomment">binomial coefficient, full definition, Matlab</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 01:18, 28 January 2022</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>== <del style="color: red; font-weight: bold; text-decoration: none;">binomial coefficient, </del>full definition, Matlab ==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>== full definition, Matlab ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>binomial coefficient from M.J. Kronenburg</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[https://arxiv.org/pdf/1105.3689.pdf]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[https://arxiv.org/pdf/1105.3689.pdf]</div></td></tr> </table>

Ranjelin http://www.convexoptimization.com/wikimization/index.php?title=Binomial_coefficient&diff=3238&oldid=prev 2022-01-28T01:16:40Z

<p>Matlab nchoosek is incomplete for negative arguments.</p> <p><b>New page</b></p><div>== binomial coefficient, full definition, Matlab ==<br /> binomial coefficient from M.J. Kronenburg<br /> [https://arxiv.org/pdf/1105.3689.pdf]<br /> <br /> Also see: [https://www.wolframalpha.com/input/?i=binomial+coefficient&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22n%22%7D+-%3E%22-10%22&amp;assumption=%7B%22F%22%2C+%22BinomialCoefficientCalculator%22%2C+%22k%22%7D+-%3E%225%22&amp;assumption=%7B%22C%22%2C+%22binomial+coefficient%22%7D+-%3E+%7B%22Calculator%22%7D Wolfram &lt;math&gt;\alpha&lt;/math&gt;]<br /> <br /> &lt;pre&gt;<br /> function y = binomial(n, k)<br /> if ~k || k == n<br /> y = 1;<br /> elseif k == 1<br /> y = n;<br /> elseif n &lt; 0<br /> if k &gt; 0<br /> y = (-1)^k*nchoosek(-n+k-1, k);<br /> elseif k &lt;= n<br /> y = (-1)^(n-k)*nchoosek(-k-1, n-k);<br /> elseif n &lt; k &amp;&amp; k &lt; 0<br /> y = 0;<br /> end<br /> elseif n &gt;= 0<br /> if k &lt; 0 || k &gt; n<br /> y = 0;<br /> else<br /> y = nchoosek(n,k);<br /> end<br /> end<br /> return<br /> &lt;/pre&gt;</div>

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