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-difference operator]], $\mathrm{Sin}_q$ is the [[Q-Sin|$q$-Sine function]], and $\mathrm{Cos}_q$ is the [[Q-Cos|$q$-cosine function]].
+
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==

Revision as of 23:25, 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