Q-exponential E sub 1/q
From specialfunctionswiki
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): ($6.153$)
