Difference between revisions of "Q-derivative"
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| − | The $q$-derivative is | + | The $q$-derivative is defined by |
| − | $$\ | + | $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} |
| − | \dfrac{f( | + | \dfrac{f(qz)-f(z)}{qz-z}, & \quad z \neq 0 \\ |
| − | f'(0) & | + | f'(0), & \quad z=0. |
\end{array} \right.$$ | \end{array} \right.$$ | ||
Revision as of 19:23, 18 December 2016
The $q$-derivative is defined by $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} \dfrac{f(qz)-f(z)}{qz-z}, & \quad z \neq 0 \\ f'(0), & \quad z=0. \end{array} \right.$$
Properties
Relationship between q-derivative and derivative
q-derivative power rule
