Difference between revisions of "Q-derivative of q-Sine"
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(Created page with "==Theorem== The following formula holds: $$D_q \mathrm{Sin}_q(bz) = b \mathrm{Cos}_q(bz),$$ where $D_q$ is the q-difference operator, $\mathrm{Sin}_q$ is the Q-Sin|$q$-S...") |
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The following formula holds: | The following formula holds: | ||
$$D_q \mathrm{Sin}_q(bz) = b \mathrm{Cos}_q(bz),$$ | $$D_q \mathrm{Sin}_q(bz) = b \mathrm{Cos}_q(bz),$$ | ||
| − | where $D_q$ is the [[q- | + | where $D_q$ is the [[q-derivative]], $\mathrm{Sin}_q$ is the [[Q-Sin|$q$-Sine function]], and $\mathrm{Cos}_q$ is the [[Q-Cos|$q$-cosine function]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=q-Cos|next=q-derivative of q-Cosine}}: (6.170) | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 23:27, 26 June 2016
Theorem
The following formula holds: $$D_q \mathrm{Sin}_q(bz) = b \mathrm{Cos}_q(bz),$$ where $D_q$ is the q-derivative, $\mathrm{Sin}_q$ is the $q$-Sine function, and $\mathrm{Cos}_q$ is the $q$-cosine function.
Proof
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.170)
