Difference between revisions of "Relationship between q-derivative and derivative"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem: The following formula holds: $$\displaystyle\lim_{q...") |
|||
| Line 1: | Line 1: | ||
<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| − | <strong>[[Relationship between q-derivative and derivative|Theorem]]: The following formula holds: | + | <strong>[[Relationship between q-derivative and derivative|Theorem]]:</strong> The following formula holds: |
$$\displaystyle\lim_{q \rightarrow 1} D_q f(x) = f'(x),$$ | $$\displaystyle\lim_{q \rightarrow 1} D_q f(x) = f'(x),$$ | ||
where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $f'(x)$ denotes the [[derivative]] of $f$. </strong> | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $f'(x)$ denotes the [[derivative]] of $f$. </strong> | ||
Revision as of 05:36, 8 February 2016
Theorem: The following formula holds: $$\displaystyle\lim_{q \rightarrow 1} D_q f(x) = f'(x),$$ where $D_q$ denotes the $q$-derivative and $f'(x)$ denotes the derivative of $f$. </strong>
Proof: █
