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Polygamma function - Revision history
2026-04-10T13:25:20Z
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en>Quondum: replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function
2014-12-08T01:15:40Z
<p>replacing redirect <a href="/index.php?title=Holomorphic&action=edit&redlink=1" class="new" title="Holomorphic (page does not exist)">Holomorphic</a> to dab page with appropriate destination <a href="/wiki/Holomorphic_function" title="Holomorphic function">Holomorphic function</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 03:15, 8 December 2014</td>
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<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><del style="font-weight: bold; text-decoration: none;">In [[mathematics]] </del>the '<del style="font-weight: bold; text-decoration: none;">''synchrotron functions''' are defined as follows (for ''x'' &ge; 0):</del></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><ins style="font-weight: bold; text-decoration: none;">The prospect encounter at all belonging to </ins>the <ins style="font-weight: bold; text-decoration: none;">restaurant, Kelly was proven to Teresa</ins>'<ins style="font-weight: bold; text-decoration: none;">s dad. 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<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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">* First synchrotron function</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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>:<<del style="font-weight: bold; text-decoration: none;">math</del>><del style="font-weight: bold; text-decoration: none;">F(x) = x \int_x^\infty K_{\frac{5}{3}}(t)\,dt</del><<del style="font-weight: bold; text-decoration: none;">/math</del>></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">* Second synchrotron function</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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>:<del style="font-weight: bold; text-decoration: none;"><math>G(x) = x K_{\frac{2}{3}}(x)<</del>/<del style="font-weight: bold; text-decoration: none;">math></del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">where ''K''<sub>''j''<</del>/<del style="font-weight: bold; text-decoration: none;">sub> is the modified [[Bessel function]</del>] of the <del style="font-weight: bold; text-decoration: none;">second kind</del>. <del style="font-weight: bold; text-decoration: none;"> The function F(x) is shown on </del>the <del style="font-weight: bold; text-decoration: none;">right, </del>as <del style="font-weight: bold; text-decoration: none;">the output from a plot </del>in [<del style="font-weight: bold; text-decoration: none;">[Mathematica]].</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">[[Image</del>:<del style="font-weight: bold; text-decoration: none;">Firstsynchfunction</del>.<del style="font-weight: bold; text-decoration: none;">jpg|thumb|First synchrotron function, F</del>(<del style="font-weight: bold; text-decoration: none;">x</del>)<del style="font-weight: bold; text-decoration: none;">]]</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;"><!-- Image </del>with <del style="font-weight: bold; text-decoration: none;">unknown copyright status removed: </del>[<del style="font-weight: bold; text-decoration: none;">[Image</del>:<del style="font-weight: bold; text-decoration: none;">secondsynchfunction</del>.<del style="font-weight: bold; text-decoration: none;">jpg|thumb|Second synchrotron function, G(x)</del>]<del style="font-weight: bold; text-decoration: none;">] --</del>></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">== Use </del>in <del style="font-weight: bold; text-decoration: none;">Astrophysics ==</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">In astrophysics</del>, <del style="font-weight: bold; text-decoration: none;">x </del>is <del style="font-weight: bold; text-decoration: none;">usually </del>a <del style="font-weight: bold; text-decoration: none;">ratio </del>of <del style="font-weight: bold; text-decoration: none;">frequencies</del>, <del style="font-weight: bold; text-decoration: none;">that is</del>, the <del style="font-weight: bold; text-decoration: none;">frequency over a critical frequency (critical frequency is the frequency </del>at <del style="font-weight: bold; text-decoration: none;">which most synchrotron radiation is radiated). This is needed when calculating the spectra for different types </del>of <del style="font-weight: bold; text-decoration: none;">synchrotron emission</del>. <del style="font-weight: bold; text-decoration: none;"> It takes a spectrum </del>of <del style="font-weight: bold; text-decoration: none;">electrons (</del>or <del style="font-weight: bold; text-decoration: none;">any charged particle) generated </del>by a <del style="font-weight: bold; text-decoration: none;">separate process (such </del>as <del style="font-weight: bold; text-decoration: none;">a power law distribution </del>of <del style="font-weight: bold; text-decoration: none;">electrons and positrons from </del>a <del style="font-weight: bold; text-decoration: none;">constant injection spectrum) and converts this </del>to <del style="font-weight: bold; text-decoration: none;">the spectrum </del>of <del style="font-weight: bold; text-decoration: none;">photons generated by the input electrons/positrons</del>.</div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">For further information</del>, <del style="font-weight: bold; text-decoration: none;">see ''High Energy Astrophysics''</del>, <del style="font-weight: bold; text-decoration: none;">Malcolm S</del>. <del style="font-weight: bold; text-decoration: none;">Longair, CUP, 1990</del>.</div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">[[Category:Special functions]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
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en>Quondum
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en>John of Reading: Typo/general fixing, replaced: additionaly → additionally using AWB
2013-08-06T14:33:55Z
<p>Typo/<a href="/index.php?title=WP:AWB/GF&action=edit&redlink=1" class="new" title="WP:AWB/GF (page does not exist)">general</a> fixing, replaced: additionaly → additionally using <a href="/index.php?title=Testwiki:AWB&action=edit&redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a></p>
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en>John of Reading
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76.120.181.41: edit
2012-09-01T22:52:29Z
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