Difference between revisions of "Q-Cos"

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The function $\mathrm{Cos}_q$ is defined by
 
The function $\mathrm{Cos}_q$ is defined by
 
$$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$
 
$$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$
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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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[[q-derivative of q-Cosine]]<br />
  
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=External links=
<strong>Theorem:</strong> The following formula holds:
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[http://homepage.tudelft.nl/11r49/documents/as98.pdf]
$$D_q \mathrm{Cos}_q(az) = -a \mathrm{Sin}_q(az),$$
 
where $D_q$ denotes the [[q-difference operator]], $\mathrm{Cos}$ denotes the [[Q-Cos|$q$-Cosine function]], and $\mathrm{Sin}$ denotes the [[Q-Sin|$q$-Sine function]].
 
<div class="mw-collapsible-content">
 
<strong>Proof:</strong> █
 
</div>
 
</div>
 
  
 
=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=Q-derivative of q-Sine}}: (6.169)
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 23:28, 26 June 2016

The function $\mathrm{Cos}_q$ is defined by $$\mathrm{Cos}_q(z)=\dfrac{E_q(iz)+E_q(-iz)}{2},$$ where $E_q$ denotes the $q$-exponential $E$.

Properties

q-Euler formula for E sub q
q-derivative of q-Cosine

External links

[1]

References