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

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==Theorem==
<strong>[[Relationship between q-derivative and derivative|Theorem]]:</strong> The following formula holds:
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The following formula holds:
$$\displaystyle\lim_{q \rightarrow 1} D_q f(x) = f'(x),$$
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$$\displaystyle\lim_{q \rightarrow 1^+} D_q f(x) = f'(x),$$
where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $f'(x)$ denotes the [[derivative]] of $f$. </strong>
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where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $f'(x)$ denotes the [[derivative]] of $f$.  
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 01:05, 25 June 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

References