Difference between revisions of "Q-exponential E sub 1/q"
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The $E_{\frac{1}{q}}$ function is defined by the formula | The $E_{\frac{1}{q}}$ function is defined by the formula | ||
| − | $$E_{\frac{1}{q}}(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k | + | $$E_{\frac{1}{q}}(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{q^{\frac{k(k-1)}{2} }}{[k]_q!} z^k.$$ |
=Properties= | =Properties= | ||
| − | < | + | [[q-exponential E sub q in terms of binomial coefficient]]<br /> |
| − | < | + | [[Q-difference equation for q-exponential E sub 1/q]]<br /> |
| − | + | ||
| − | + | =See Also= | |
| − | + | [[Q-exponential E sub q]]<br /> | |
| − | + | ||
| − | + | =References= | |
| − | + | * {{BookReference|Quantum Calculus|2002|Victor Kac|author2=Pokman Cheung||prev=findme|next=findme}} $(9.10)$ (calls $E_{\frac{1}{q}}(x)$ $E_q^x$) | |
| + | * {{BookReference|A Comprehensive Treatment of q-Calculus|2012|Thomas Ernst|prev=Q-difference equation for q-exponential E sub q|next=Q-difference equation for q-exponential E sub 1/q}}: ($6.153$) | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 04:30, 26 December 2016
The $E_{\frac{1}{q}}$ function is defined by the formula $$E_{\frac{1}{q}}(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{q^{\frac{k(k-1)}{2} }}{[k]_q!} z^k.$$
Properties
q-exponential E sub q in terms of binomial coefficient
Q-difference equation for q-exponential E sub 1/q
See Also
References
- 2002: Victor Kac and Pokman Cheung: Quantum Calculus ... (previous) ... (next) $(9.10)$ (calls $E_{\frac{1}{q}}(x)$ $E_q^x$)
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.153$)
