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-factorial|$q$-factorial]].
+
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.

Proof

References