# Difference between revisions of "Q-derivative power rule"

From specialfunctionswiki

(One intermediate revision by the same user not shown) | |||

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== | ||

==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.