Difference between revisions of "Q-derivative power rule"
From specialfunctionswiki
| Line 2: | Line 2: | ||
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== | ||
Revision as of 18:28, 20 September 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.
