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 | + | __NOTOC__ |
| − | $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2} | + | The function $\cos_q$ is defined for $|z|<1$ by |
| + | $$\cos_q(z)=\dfrac{e_q(iz)+e_q(-iz)}{2},$$ | ||
| + | where $e_q$ denotes the [[q-exponential e|$q$-exponential $e$]] and $(q;q)_{2k}$ denotes the [[q-Pochhammer|$q$-Pochhammer symbol]]. | ||
=Properties= | =Properties= | ||
| − | + | [[q-Euler formula for e sub q]]<br /> | |
| + | |||
| + | =External links= | ||
| + | [http://homepage.tudelft.nl/11r49/documents/as98.pdf] | ||
=References= | =References= | ||
| − | [ | + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=q-sin sub q|next=}}: $(6.202)$ |
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 15:37, 11 July 2016
The function $\cos_q$ is defined for $|z|<1$ by $$\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
External links
References
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous): $(6.202)$
