http://specialfunctionswiki.org/index.php?title=Logarithmic_derivative_of_Jacobi_theta_3_equals_a_sum_of_sines&feed=atom&action=history
Logarithmic derivative of Jacobi theta 3 equals a sum of sines - Revision history
2024-03-29T09:43:59Z
Revision history for this page on the wiki
MediaWiki 1.28.0
http://specialfunctionswiki.org/index.php?title=Logarithmic_derivative_of_Jacobi_theta_3_equals_a_sum_of_sines&diff=7057&oldid=prev
Tom at 18:04, 5 July 2016
2016-07-05T18:04:46Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;' lang='en'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 18:04, 5 July 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7" >Line 7:</td>
<td colspan="2" class="diff-lineno">Line 7:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines|next=Logarithmic derivative of Jacobi theta 4 equals a sum of sines}}: 16.29.3</div></td><td class='diff-marker'>+</td><td style="color:black; 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>* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines|next=Logarithmic derivative of Jacobi theta 4 equals a sum of sines}}: <ins class="diffchange diffchange-inline">$</ins>16.29.3<ins class="diffchange diffchange-inline">$</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Theorem]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Theorem]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Unproven]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Unproven]]</div></td></tr>
</table>
Tom
http://specialfunctionswiki.org/index.php?title=Logarithmic_derivative_of_Jacobi_theta_3_equals_a_sum_of_sines&diff=6887&oldid=prev
Tom: Created page with "==Theorem== The following formula holds: $$\dfrac{\vartheta_3'(u,q)}{\vartheta_3(u,q)} = 4\displaystyle\sum_{k=1}^{\infty} (-1)^k \dfrac{q^k}{1-q^{2k}} \sin(2ku),$$ where $\v..."
2016-06-27T07:17:01Z
<p>Created page with "==Theorem== The following formula holds: $$\dfrac{\vartheta_3'(u,q)}{\vartheta_3(u,q)} = 4\displaystyle\sum_{k=1}^{\infty} (-1)^k \dfrac{q^k}{1-q^{2k}} \sin(2ku),$$ where $\v..."</p>
<p><b>New page</b></p><div>==Theorem==<br />
The following formula holds:<br />
$$\dfrac{\vartheta_3'(u,q)}{\vartheta_3(u,q)} = 4\displaystyle\sum_{k=1}^{\infty} (-1)^k \dfrac{q^k}{1-q^{2k}} \sin(2ku),$$<br />
where $\vartheta_3$ denotes the [[Jacobi theta 3]] and $\sin$ denotes the [[sine]].<br />
<br />
==Proof==<br />
<br />
==References==<br />
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithmic derivative of Jacobi theta 2 equals negative tangent + a sum of sines|next=Logarithmic derivative of Jacobi theta 4 equals a sum of sines}}: 16.29.3<br />
<br />
[[Category:Theorem]]<br />
[[Category:Unproven]]</div>
Tom