Difference between revisions of "Q-sin sub q"
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| − | The function $\sin_q$ is defined by | + | The function $\sin_q$ is defined for $|z|<1$ by |
| − | $$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i | + | $$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i},$$ |
where $e_q$ denotes the [[q-exponential e|$q$-exponential $e$]] and $(q;q)_{2k+1}$ denotes the [[q-Pochhammer|$q$-Pochhammer symbol]]. | where $e_q$ denotes the [[q-exponential e|$q$-exponential $e$]] and $(q;q)_{2k+1}$ denotes the [[q-Pochhammer|$q$-Pochhammer symbol]]. | ||
=Properties= | =Properties= | ||
| − | + | [[q-Euler formula for e sub q]]<br /> | |
| + | [[Series for q-sin sub q]]<br /> | ||
| + | |||
| + | =External links= | ||
| + | [http://homepage.tudelft.nl/11r49/documents/as98.pdf] | ||
=References= | =References= | ||
| − | + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=findme|next=Series for q-sin sub q}}: $(6.201)$ | |
| + | |||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 15:39, 11 July 2016
The function $\sin_q$ is defined for $|z|<1$ by $$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i},$$ where $e_q$ denotes the $q$-exponential $e$ and $(q;q)_{2k+1}$ denotes the $q$-Pochhammer symbol.
Properties
q-Euler formula for e sub q
Series for q-sin sub q
External links
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): $(6.201)$
