Difference between revisions of "Q-Sin"
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(Created page with "The function $\mathrm{Sin}_q$ is defined by $$\mathrm{Sin}_q(z)=\dfrac{E_q(iz)-E_q(-iz)}{2i},$$ where $E_q$ denotes the $q$-exponential $E$. =Properties=...") |
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The function $\mathrm{Sin}_q$ is defined by | The function $\mathrm{Sin}_q$ is defined by | ||
$$\mathrm{Sin}_q(z)=\dfrac{E_q(iz)-E_q(-iz)}{2i},$$ | $$\mathrm{Sin}_q(z)=\dfrac{E_q(iz)-E_q(-iz)}{2i},$$ | ||
| − | where $E_q$ denotes the [[q-exponential E|$q$-exponential $ | + | where $E_q$ denotes the [[q-exponential E sub q|$q$-exponential $E_q$]]. |
=Properties= | =Properties= | ||
| − | + | [[q-Euler formula for E sub q]]<br /> | |
| + | [[q-derivative of q-Sine]]<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=q-Cos}}: (6.168) |
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 00:49, 15 September 2016
The function $\mathrm{Sin}_q$ is defined by $$\mathrm{Sin}_q(z)=\dfrac{E_q(iz)-E_q(-iz)}{2i},$$ where $E_q$ denotes the $q$-exponential $E_q$.
Properties
q-Euler formula for E sub q
q-derivative of q-Sine
External links
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.168)
