Difference between revisions of "Q-cos sub q"

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(Created page with "The function $\cos_q$ is defined by $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2}=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k}}{(q;q)_{2k}}.$$ =Properties= {{:q-Euler formu...")
 
 
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The function $\cos_q$ is defined by
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__NOTOC__
$$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2}=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k}}{(q;q)_{2k}}.$$
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The function $\cos_q$ is defined for $|z|<1$ by
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$$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2},$$
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where $e_q$ denotes the [[q-exponential e|$q$-exponential $e$]] and $(q;q)_{2k}$ 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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=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=q-sin sub q|next=}}: $(6.202)$
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[[Category:SpecialFunction]]

Latest revision as of 15:37, 11 July 2016

The function $\cos_q$ is defined for $|z|<1$ by $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2},$$ where $e_q$ denotes the $q$-exponential $e$ and $(q;q)_{2k}$ denotes the $q$-Pochhammer symbol.

Properties

q-Euler formula for e sub q

External links

[1]

References