Difference between revisions of "Q-exponential E sub 1/q"
From specialfunctionswiki
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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.$$ |
=Properties= | =Properties= | ||
| + | [[q-exponential E sub q in terms of binomial coefficient]]<br /> | ||
[[Q-difference equation for q-exponential E sub 1/q]]<br /> | [[Q-difference equation for q-exponential E sub 1/q]]<br /> | ||
Revision as of 04:02, 21 December 2016
The $E_{\frac{1}{q}}$ function is defined by the formula $$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
- 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.153$)
