Difference between revisions of "Relationship between q-derivative and derivative"
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| − | + | ==Theorem== | |
| − | + | 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 $f$. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[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 $f$.
