Difference between revisions of "Q-derivative"
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Revision as of 22:06, 2 May 2015
The $q$-derivative is $$D_q\{f\}(x)=\left(\dfrac{d}{dx} \right)_q f(x) = \dfrac{f(qx)-f(x)}{qx-x}.$$
Contents
Properties
Theorem
The following formula holds: $$D_q(z^n)=[n]_q z^{n-1},$$ where $D_q$ denotes the $q$-derivative and $[n]_q$ denotes the $q$-number.
