Difference between revisions of "Q-derivative power rule"

From specialfunctionswiki
Jump to: navigation, search
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-factorial|$q$-factorial]].
+
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.

Proof

References