Difference between revisions of "Q-derivative power rule"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$D_q(z^n)=[n]_q z^{n-1},$$ where $D_q$...") |
|||
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | 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-factorial|$q$-factorial]]. | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $[n]_q$ denotes the [[q-factorial|$q$-factorial]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 22:31, 16 June 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 $q$-factorial.
