Difference between revisions of "Relationship between q-derivative and derivative"

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<strong>[[Relationship between q-derivative and derivative|Theorem]]:</strong> 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 $f$.  
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 
<strong>Proof: █  
 
<strong>Proof: █  
 
</div>
 
</div>
 
</div>
 
</div>

Revision as of 05:37, 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 $f$.

Proof: █ </div> </div>