Limit of q-exponential E sub 1/q for 0 less than q less than 1

Theorem

The following formula holds for $0 < q < 1$: $$\displaystyle\lim_{t \rightarrow \infty} E_{\frac{1}{q}}(t)=\infty,$$ where $E_{\frac{1}{q}}$ denotes the $q$-exponential $E_{\frac{1}{q}}$.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): ($6.156$)