Difference between revisions of "Q-cos sub q"

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=Properties=
 
=Properties=
 
[[q-Euler formula for e sub q]]<br />
 
[[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|next=}}: $(6.202)$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 15:35, 11 July 2016

The function $\cos_q$ is defined by $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2}=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kz^{2k}}{(q;q)_{2k}},$$ 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