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.$$ | \end{array} \right.$$ | ||
| + | where $f'(0)$ denotes the [[derivative]]. | ||
=Properties= | =Properties= | ||
| Line 10: | Line 11: | ||
=References= | =References= | ||
| + | * {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=findme|next=Q-derivative power rule}} $(2.1)$ | ||
| + | * {{BookReference|Quantum Calculus|2002|Victor Kac|author2=Pokman Cheung||prev=findme|next=findme}} $(1.5)$ | ||
Latest revision as of 04:05, 26 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
References
- D.S. McAnally: q-exponential and q-gamma functions. I. q-exponential functions (1994)... (previous)... (next) $(2.1)$
- 2002: Victor Kac and Pokman Cheung: Quantum Calculus ... (previous) ... (next) $(1.5)$
