Difference between revisions of "Q-derivative power rule"
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The following formula holds: | The following formula holds: | ||
$$D_q(z^n)=[n]_q z^{n-1},$$ | $$D_q(z^n)=[n]_q z^{n-1},$$ | ||
| − | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $[n]_q$ denotes the [[q- | + | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $[n]_q$ denotes the [[q-number|$q$-number]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{PaperReference|q-exponential and q-gamma functions. I. q-exponential functions|1994|D.S. McAnally|prev=q-Derivative|next=q-number}} $(2.2)$ | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 19:37, 18 December 2016
Theorem
The following formula holds: $$D_q(z^n)=[n]_q z^{n-1},$$ where $D_q$ denotes the $q$-derivative and $[n]_q$ denotes the $q$-number.
