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 $f$. | where $D_q$ denotes the [[q-derivative|$q$-derivative]] and $f'(x)$ denotes the [[derivative]] of $f$. | ||
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Revision as of 05:38, 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>
