Difference between revisions of "Q-sin sub q"

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The function $\sin_q$ is defined by
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The function $\sin_q$ is defined for $|z|<1$ by
$$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i} = \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k+1}}{(q;q)_{2k+1}},$$
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$$\sin_q(z)=\dfrac{e_q(iz)-e_q(-iz)}{2i},$$
 
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}}
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[[q-Euler formula for e sub q]]<br />
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[[Series for q-sin sub q]]<br />
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=External links=
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[http://homepage.tudelft.nl/11r49/documents/as98.pdf]
  
 
=References=
 
=References=
[http://homepage.tudelft.nl/11r49/documents/as98.pdf]
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* {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=findme|next=Series for q-sin sub q}}: $(6.201)$
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[[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

[1]

References