Difference between revisions of "Q-derivative"
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$$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} | $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} | ||
\dfrac{f(qz)-f(z)}{qz-z}, & \quad z \neq 0 \\ | \dfrac{f(qz)-f(z)}{qz-z}, & \quad z \neq 0 \\ | ||
| − | f'(0), & \quad z=0 | + | f'(0), & \quad z=0, |
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | where $f'(0)$ denotes the [[derivative]]. | ||
=Properties= | =Properties= | ||
Revision as of 19:25, 18 December 2016
The $q$-derivative is defined by $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} \dfrac{f(qz)-f(z)}{qz-z}, & \quad z \neq 0 \\ f'(0), & \quad z=0, \end{array} \right.$$ where $f'(0)$ denotes the derivative.
Properties
Relationship between q-derivative and derivative
q-derivative power rule
