Difference between revisions of "Q-derivative"
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The $q$-derivative is defined by | The $q$-derivative is defined by | ||
$$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} | $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} | ||
| − | \dfrac{f(qz)-f(z)}{ | + | \dfrac{f(qz)-f(z)}{(q-1)z}, & \quad z \neq 0 \\ |
f'(0), & \quad z=0, | f'(0), & \quad z=0, | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| Line 11: | Line 11: | ||
=References= | =References= | ||
| − | * {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|next= | + | * {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=findme|next=Q-derivative power rule}} $(2.1)$ |
Revision as of 19:36, 18 December 2016
The $q$-derivative is defined by $$\dfrac{\mathrm{d}_qf}{\mathrm{d}_qz}=\left\{ \begin{array}{ll} \dfrac{f(qz)-f(z)}{(q-1)z}, & \quad z \neq 0 \\ f'(0), & \quad z=0, \end{array} \right.$$ where $f'(0)$ denotes the derivative.
Properties
Relationship between q-derivative and derivative
q-derivative power rule
