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Formula:KLS:01.15:01 - Revision history
2024-03-29T08:19:30Z
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imported>SeedBot: DRMF
2017-03-05T22:34:39Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:KLS:01.15:01}}<br />
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<div id="alignleft"> << [[Some_q-analogues_of_special_functions|Some q-analogues of special functions]] </div><br />
<div id="aligncenter"> [[The_q-derivative_and_q-integral#KLS:01.15:01|formula in The q-derivative and q-integral]] </div><br />
<div id="alignright"> [[Formula:KLS:01.15:02|Formula:KLS:01.15:02]] >> </div><br />
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<br /><div align="center"><math>{\displaystyle <br />
\index{q-Derivative operator@$q$-Derivative operator}<br />
\qderiv{q}f(z):=\left\{\begin{array}{ll}<br />
\displaystyle \frac{f(z)-f(qz)}{(1-q)z}, & z\neq 0\\[5mm]<br />
f'(0), & z=0.\end{array}\right.<br />
}</math></div><br />
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== Proof ==<br />
<br />
We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.<br />
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== Symbols List ==<br />
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& : logical and<br /><br />
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:qderiv <math>{\displaystyle \mathcal{D}_q^n}</math>]</span> : <math>{\displaystyle q}</math>-derivative : [http://drmf.wmflabs.org/wiki/Definition:qderiv http://drmf.wmflabs.org/wiki/Definition:qderiv]<br />
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== Bibliography==<br />
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<span class="plainlinks">[http://homepage.tudelft.nl/11r49/askey/contents.html Equation in Section 1.15]</span> of [[Bibliography#KLS|'''KLS''']].<br />
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== URL links ==<br />
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<br /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Some_q-analogues_of_special_functions|Some q-analogues of special functions]] </div><br />
<div id="aligncenter"> [[The_q-derivative_and_q-integral#KLS:01.15:01|formula in The q-derivative and q-integral]] </div><br />
<div id="alignright"> [[Formula:KLS:01.15:02|Formula:KLS:01.15:02]] >> </div><br />
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