http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&feed=atom&action=history
Nth root of nonnegative integers - Revision history
2024-03-28T12:38:52Z
Revision history for this page on the wiki
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http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1465&oldid=prev
Tom at 00:56, 11 December 2016
2016-12-11T00:56:29Z
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Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1046&oldid=prev
Tom at 22:41, 23 February 2016
2016-02-23T22:41:20Z
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Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1039&oldid=prev
Tom at 22:27, 23 February 2016
2016-02-23T22:27:16Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 22:27, 23 February 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l29" >Line 29:</td>
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<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>|[[Delta integral | $\Delta$-integral]]</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>|[[Delta integral | $\Delta$-integral]]</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>|$\displaystyle\int_s^t f(\tau) \Delta \tau=$</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>|$\displaystyle\int_s^t f(\tau) \Delta \tau=<ins class="diffchange diffchange-inline">\displaystyle\sum_{k=s^n}^{t^n-1} (\sqrt[n]{k+1}-\sqrt[n]{k}) f(\sqrt[n]{k})</ins>$</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;"><div>|[[Derivation of delta integral for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of delta integral for T=nth root of nonnegative integers|derivation]]</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1038&oldid=prev
Tom at 22:22, 23 February 2016
2016-02-23T22:22:17Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 22:22, 23 February 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21" >Line 21:</td>
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<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>|[[Delta derivative | $\Delta$-derivative]]</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>|[[Delta derivative | $\Delta$-derivative]]</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>|$f^{\Delta}(t)=$</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>|$f^{\Delta}(t)=<ins class="diffchange diffchange-inline">\dfrac{f(\sqrt[n]{t^n+1})-f(t)}{\sqrt[n]{t^n+1}-t}</ins>$</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;"><div>|[[Derivation of delta derivative for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of delta derivative for T=nth root of nonnegative integers|derivation]]</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>|-</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>|-</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>|[[Nabla derivative | $\nabla$-derivative]]</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>|[[Nabla derivative | $\nabla$-derivative]]</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>|$f^{\nabla}(t)=$</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>|$f^{\nabla}(t)=<ins class="diffchange diffchange-inline">\dfrac{f(t)-f(\sqrt[n]{t^n-1})}{t-\sqrt{t^n-1}}</ins>$</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;"><div>|[[Derivation of nabla derivative for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of nabla derivative for T=nth root of nonnegative integers|derivation]]</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1037&oldid=prev
Tom at 22:18, 23 February 2016
2016-02-23T22:18:39Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 22:18, 23 February 2016</td>
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<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>|[[Backward graininess]]:</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>|[[Backward graininess]]:</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>|$\nu(t)=$</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>|$\nu(t)=<ins class="diffchange diffchange-inline">t-\sqrt[n]{t^n-1}</ins>$</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;"><div>|[[Derivation of backward graininess for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of backward graininess for T=nth root of nonnegative integers|derivation]]</div></td></tr>
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Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1036&oldid=prev
Tom at 22:18, 23 February 2016
2016-02-23T22:18:18Z
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 22:18, 23 February 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</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>The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a [[time scale]].</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><ins class="diffchange diffchange-inline">Let $n \in \{1,2,\ldots\}$. </ins>The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a [[time scale]].</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>{| class="wikitable"</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>{| class="wikitable"</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5" >Line 5:</td>
<td colspan="2" class="diff-lineno">Line 5:</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>|-</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>|-</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>|[[Forward jump]]:</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>|[[Forward jump]]:</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>|$\sigma(t)=$</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>|$\sigma(t)=<ins class="diffchange diffchange-inline">\sqrt[n]{t^n+1}</ins>$</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;"><div>|[[Derivation of forward jump for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of forward jump for T=nth root of nonnegative integers|derivation]]</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>|-</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>|-</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>|[[Forward graininess]]:</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>|[[Forward graininess]]:</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>|$\mu(t)=$</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>|$\mu(t)=<ins class="diffchange diffchange-inline">\sqrt[n]{t^n+1}-t</ins>$</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;"><div>|[[Derivation of forward graininess for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of forward graininess for T=nth root of nonnegative integers|derivation]]</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>|-</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>|-</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>|[[Backward jump]]:</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>|[[Backward jump]]:</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>|$\rho(t)=$</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>|$\rho(t)=<ins class="diffchange diffchange-inline">\sqrt[n]{t^n-1}</ins>$</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;"><div>|[[Derivation of backward jump for T=nth root of nonnegative integers|derivation]]</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>|[[Derivation of backward jump for T=nth root of nonnegative integers|derivation]]</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>|-</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>|-</div></td></tr>
</table>
Tom
http://timescalewiki.org/index.php?title=Nth_root_of_nonnegative_integers&diff=1035&oldid=prev
Tom: Created page with "The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a time scale. {| class="wikitable" |+$\mathbb{T}=\sqrt[n]{\mathbb{N}}$ |- |Forward jump: |..."
2016-02-23T22:16:47Z
<p>Created page with "The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a <a href="/index.php/Time_scale" title="Time scale">time scale</a>. {| class="wikitable" |+$\mathbb{T}=\sqrt[n]{\mathbb{N}}$ |- |<a href="/index.php/Forward_jump" title="Forward jump">Forward jump</a>: |..."</p>
<p><b>New page</b></p><div>The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a [[time scale]].<br />
<br />
{| class="wikitable"<br />
|+$\mathbb{T}=\sqrt[n]{\mathbb{N}}$<br />
|-<br />
|[[Forward jump]]:<br />
|$\sigma(t)=$<br />
|[[Derivation of forward jump for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Forward graininess]]:<br />
|$\mu(t)=$<br />
|[[Derivation of forward graininess for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Backward jump]]:<br />
|$\rho(t)=$<br />
|[[Derivation of backward jump for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Backward graininess]]:<br />
|$\nu(t)=$<br />
|[[Derivation of backward graininess for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta derivative | $\Delta$-derivative]]<br />
|$f^{\Delta}(t)=$<br />
|[[Derivation of delta derivative for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla derivative | $\nabla$-derivative]]<br />
|$f^{\nabla}(t)=$<br />
|[[Derivation of nabla derivative for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta integral | $\Delta$-integral]]<br />
|$\displaystyle\int_s^t f(\tau) \Delta \tau=$<br />
|[[Derivation of delta integral for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla integral | $\nabla$-integral]]<br />
|$\displaystyle\int_s^t f(\tau) \nabla \tau=$<br />
|[[Derivation of nabla integral for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta hk|$h_k(t,s)$]]<br />
|$h_k(t,s)=$<br />
|[[Derivation of delta hk for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla hk|$\hat{h}_k(t,s)$]]<br />
|$\hat{h}_k(t,s)=$<br />
|[[Derivation of nabla hk for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta gk|$g_k(t,s)$]]<br />
|$g_k(t,s)=$<br />
|[[Derivation of delta gk for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla gk|$\hat{g}_k(t,s)$]]<br />
|$\hat{g}_k(t,s)=$<br />
|[[Derivation of nabla gk for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta exponential | $e_p(t,s)$]] <br />
|$e_p(t,s)=$<br />
|[[Derivation of delta exponential T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla exponential | $\hat{e}_p(t,s)$]]<br />
|$\hat{e}_p(t,s)=$<br />
|[[Derivation of nabla exponential T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Gaussian bell]]<br />
|$\mathbf{E}(t)=$<br />
|[[Derivation of Gaussian bell for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta sine | $\mathrm{sin}_p(t,s)=$]]<br />
|$\sin_p(t,s)=$<br />
|[[Derivation of delta sin sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|$\mathrm{\sin}_1(t,s)$<br />
|$\sin_1(t,s)=$<br />
|[[Derivation of delta sin sub 1 for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla sine|$\widehat{\sin}_p(t,s)$]]<br />
|$\widehat{\sin}_p(t,s)=$<br />
|[[Derivation of nabla sine sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta cosine|$\mathrm{\cos}_p(t,s)$]]<br />
|$\cos_p(t,s)=$<br />
|[[Derivation of delta cos sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|$\mathrm{\cos}_1(t,s)$<br />
|$\cos_1(t,s)=$<br />
|[[Derivation of delta cos sub 1 for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla cosine|$\widehat{\cos}_p(t,s)$]]<br />
|$\widehat{\cos}_p(t,s)=$<br />
|[[Derivation of nabla cos sub 1 for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta sinh|$\sinh_p(t,s)$]]<br />
|$\sinh_p(t,s)=$<br />
|[[Derivation of delta sinh sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla sinh|$\widehat{\sinh}_p(t,s)$]]<br />
|$\widehat{\sinh}_p(t,s)=$<br />
|[[Derivation of nabla sinh sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Delta cosh|$\cosh_p(t,s)$]]<br />
|$\cosh_p(t,s)=$<br />
|[[Derivation of delta cosh sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Nabla cosh|$\widehat{\cosh}_p(t,s)$]]<br />
|$\widehat{\cosh}_p(t,s)=$<br />
|[[Derivation of nabla cosh sub p for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Gamma function]]<br />
|$\Gamma_{\sqrt[n]{\mathbb{N}}}(x,s)=$<br />
|[[Derivation of gamma function for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Euler-Cauchy logarithm]]<br />
|$L(t,s)=$<br />
|[[Derivation of Euler-Cauchy logarithm for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Bohner logarithm]]<br />
|$L_p(t,s)=$<br />
|[[Derivation of the Bohner logarithm for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Jackson logarithm]]<br />
|$\log_{\sqrt[n]{\mathbb{N}}} g(t)=$<br />
|[[Derivation of the Jackson logarithm for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Mozyrska-Torres logarithm]]<br />
|$L_{\sqrt[n]{\mathbb{N}}}(t)=$<br />
|[[Derivation of the Mozyrska-Torres logarithm for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Laplace transform]]<br />
|$\mathscr{L}_{\sqrt[n]{\mathbb{N}}}\{f\}(z;s)=$<br />
|[[Derivation of Laplace transform for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|[[Hilger circle]] <br />
|<br />
|[[Derivation of Hilger circle for T=nth root of nonnegative integers|derivation]]<br />
|-<br />
|}</div>
Tom