Q-derivative

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

• {{ #if: |{{{2}}}|D.S. McAnally}}{{#if: |{{#if: |, [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]}}|}}: [[Paper:D.S. McAnally/q-exponential and q-gamma functions. I. q-exponential functions{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|q-exponential and q-gamma functions. I. q-exponential functions{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}} (1994)| ({{#if: |{{{ed}}} ed., }}1994)}}]]{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: findme | ... (previous)|}}{{#if: Q-derivative power rule | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}} $(2.1)$
• 2002: {{ #if: |{{{2}}}|Victor Kac}}{{#if: Pokman Cheung|{{#if: |, {{ #if: |{{{2}}}|Pokman Cheung}}{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and {{ #if: |{{{2}}}|Pokman Cheung}}}}|}}: [[Book:Victor Kac/Quantum Calculus{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|Quantum Calculus{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: findme | ... (previous)|}}{{#if: findme | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}} $(1.5)$