Difference between revisions of "Q-derivative of q-Cosine"
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(Created page with "==Theorem== The following formula holds: $$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$ where $D_q$ denotes the q-difference operator, $\mathrm{Cos}$ denotes the Q-...") |
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The following formula holds: | The following formula holds: | ||
$$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$ | $$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$ | ||
| − | where $D_q$ denotes the [[q- | + | where $D_q$ denotes the [[q-derivative]], $\mathrm{Cos}$ denotes the [[Q-Cos|$q$-Cosine function]], and $\mathrm{Sin}$ denotes the [[Q-Sin|$q$-Sine function]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=Q-derivative of q-Sine|next=findme}}: (6.171) | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:29, 26 June 2016
Theorem
The following formula holds: $$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$ where $D_q$ denotes the q-derivative, $\mathrm{Cos}$ denotes the $q$-Cosine function, and $\mathrm{Sin}$ denotes the $q$-Sine function.
Proof
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.171)
